Introduction to Management Science, 12E Bernard W Taylor Test Bank by Ace Test Banks

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Introduction to Management Science 12th Edition Geoff Willis University of Central Oklahoma College of Business

Bernard W. Taylor III Virginia Polytechnic Institute and State University

Introduction to Management Science, 12e (Taylor) Chapter 1 Management Science 1) A management science solution can be either a recommended decision or information that helps a manager make a decision. Answer: TRUE Diff: 2 Page Ref: 5 Section Heading: The Management Science Approach to Problem Solving Keywords: model, management science techniques AACSB: Analytical thinking

2) A variable is a value that is usually a coefficient of a parameter in an equation. Answer: FALSE Diff: 1 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: variable AACSB: Analytical thinking

3) Parameters are known, constant values that are usually coefficients of variables in equations. Answer: TRUE Diff: 1 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: parameter AACSB: Analytical thinking

4) Data are pieces of information from the problem environment. Answer: TRUE Diff: 1 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: data AACSB: Analytical thinking

5) A model is a mathematical representation of a problem situation including variables, parameters, and equations. Answer: TRUE Diff: 1 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: model, management science techniques AACSB: Analytical thinking

6) A management science technique usually applies to a specific model type. Answer: TRUE Diff: 1 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: models, management science techniques AACSB: Analytical thinking

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7) The first step of the management science process is to define the problem. Answer: FALSE Diff: 2 Page Ref: 2 Section Heading: The Management Science Approach to Problem Solving Keywords: management science process AACSB: Analytical thinking

8) The term big data refers to numbers of large magnitude, i.e., greater than or equal to one billion. Answer: FALSE Diff: 1 Page Ref: 7 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge

9) A key component of business analytics is the recent availability of large amounts of data. Answer: TRUE Diff: 1 Page Ref: 7 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge

10) Business analytics brings together the disciplines of information systems, management science, statistics, and mathematical modeling. Answer: TRUE Diff: 1 Page Ref: 7 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge

11) Management science modeling techniques provide results that are known with certainty. Answer: FALSE Diff: 2 Page Ref: 17 Section Heading: Management Science Modeling Techniques Keywords: management science modeling techniques, certainty AACSB: Analytical thinking

12) The term "sensitivity analysis" refers to testing how a problem solution reacts to changes in one or more of the model parameters. Answer: TRUE Diff: 1 Page Ref: 11 Section Heading: Model Building: Break-Even Analysis Keywords: sensitivity analysis, parameter changes AACSB: Application of knowledge

13) Variable costs depend on the number of items produced. Answer: TRUE Diff: 1 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: variable cost, break-even analysis AACSB: Application of knowledge

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14) Fixed cost is the difference between total cost and total variable cost. Answer: TRUE Diff: 1 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: total cost, break-even analysis AACSB: Application of knowledge

15) The break-even point is the volume that equates total revenue with total cost. Answer: TRUE Diff: 1 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

16) In general, an increase in price increases the break-even point if all costs are held constant. Answer: FALSE Diff: 1 Page Ref: 11 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

17) If variable costs increase, but price and fixed costs are held constant, the break-even point will decrease. Answer: FALSE Diff: 2 Page Ref: 11 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

18) Managers utilize spreadsheets to conduct their own analyses in management science studies. Answer: TRUE Diff: 2 Page Ref: 13 Section Heading: Computer Solution Keywords: spreadsheets AACSB: Analytical thinking

19) Management science techniques focus primarily on observation, model construction, and implementation to find an appropriate solution to a problem. Answer: FALSE Diff: 2 Page Ref: 16 Section Heading: Management Science Modeling Techniques Keywords: mgt science modeling techniques, steps of the scientific method AACSB: Analytical thinking

20) Management science modeling techniques focus on model construction and problem solution. Answer: TRUE Diff: 2 Page Ref: 15 Section Heading: Management Science Modeling Techniques Keywords: mgt science model techniques, model constr, prob solution AACSB: Analytical thinking

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21) A typical objective function might be written as 3S + 2R + 5Z ≤ 20. Answer: FALSE Diff: 2 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function AACSB: Analytical thinking

22) Decision Support Systems (DSS) use computers to help decision makers address complex problems. Answer: TRUE Diff: 1 Page Ref: 20 Section Heading: Management Science Models in Decision Support Systems Keywords: decision making, management science AACSB: Application of knowledge

23) In both an objective function and a constraint, the decision variables are represented by numbers. Answer: FALSE Diff: 1 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: decision variables AACSB: Analytical thinking

24) Constraints usually appear as equations that are less than, equal to, or greater than a parameter. Answer: TRUE Diff: 1 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints AACSB: Analytical thinking

25) A key element of a decision support system (DSS) is the person using the system. Answer: TRUE Diff: 2 Page Ref: 20 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking

26) ________ are pieces of information from the problem environment. Answer: Data Diff: 1 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: data AACSB: Application of knowledge

27) A ________ is a functional relationship including variables, parameters, and equations. Answer: model Diff: 1 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: model AACSB: Application of knowledge

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28) ________ is the term used to describe a collection of numbers that is massive in size. Answer: Big data Diff: 1 Page Ref: 7 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge

29) ________ uses large amounts of data with management science techniques and modeling to help managers make decisions. Answer: Business analytics Diff: 1 Page Ref: 7 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge

30) Management science techniques include ________ techniques, models that are represented as diagrams, presenting a pictorial representation of the system being analyzed. Answer: network Diff: 1 Page Ref: 17 Section Heading: Management Science Modeling Techniques Keywords: management science, networks AACSB: Application of knowledge

31) An increase in output typically results in an increase in the ________ cost. Answer: total variable, total Diff: 1 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

32) ________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic. Answer: Probabilistic Diff: 1 Page Ref: 17 Section Heading: Management Science Modeling Techniques Keywords: management science techniques, probabilistic techniques AACSB: Analytical thinking

33) ________ costs are independent of the volume of goods produced and remain constant. Answer: Fixed Diff: 1 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: fixed cost, break-even analysis AACSB: Analytical thinking

34) Total revenue minus total cost equals ________. Answer: profit Diff: 1 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: profit, break-even analysis AACSB: Analytical thinking

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35) The ________ is the volume that equates total revenue with total cost. Answer: break-even point Diff: 1 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

36) A ________ represents a limitation to achieving maximum profits due to limited resources. Answer: constraint Diff: 1 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: constraint, model development AACSB: Analytical thinking

37) One way to test how a management science model reacts to changes in its parameters is to conduct ________ analysis. Answer: sensitivity Diff: 1 Page Ref: 11 Section Heading: Model Building: Break-Even Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

38) ________ consist of models that are represented as diagrams rather than as strictly mathematical techniques. Answer: Networks Diff: 2 Page Ref: 17 Section Heading: Management Science Modeling Techniques Keywords: network flow models AACSB: Analytical thinking

39) A management science technique that does not assume that all parameters are known with certainty is a(n) ________ technique. Answer: probabilistic Diff: 2 Page Ref: 17 Section Heading: Management Science Modeling Techniques Keywords: probabilistic techniques AACSB: Analytical thinking

40) A ________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations. Answer: decision support system Diff: 1 Page Ref: 20 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking

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41) The relationship d = 5000 - 25p describes what happens to demand (d) as price (p) varies. Price can vary between $10 and $50. How many units can be sold when the price is $10? Answer: 4750 Diff: 2 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: break-even analysis AACSB: Analytical thinking

42) A production process requires a fixed cost of $50,000 and the variable cost per unit is $25. The revenue per unit was projected to be $45, but a recent marketing study shows that because of an emerging competitor, the revenue will be about 12% lower. How does this affect the break-even point? Answer: The break-even point will be higher, at 3424 units, which is a 37% increase. Diff: 3 Page Ref: 11 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

43) Administrators at a university are planning to offer a summer seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? Answer: $175 Diff: 2 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

44) A newly opened bed-and-breakfast projects the following: Monthly fixed costs Variable cost per occupied room per night Revenue per occupied room per night

$8000 $40 $165

Write the expression for total cost per month. Answer: C(x) = 8000 + 40x Diff: 2 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

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45) A newly opened bed-and-breakfast projects the following: Monthly fixed costs Variable cost per occupied room per night Revenue per occupied room per night

$8000 $40 $165

Write the expression for total revenue per month. Answer: R(x) = 165x Diff: 2 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

46) A newly opened bed-and-breakfast projects the following: Monthly fixed costs Variable cost per occupied room per night Revenue per occupied room per night

$8000 $40 $165

How many rooms would have to be occupied per month in order to break even? Answer: 64 rooms Diff: 2 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

47) A script writer has received an advance against royalties of $10,000. The royalty rate is $2 for every performance in the U.S., and $3 for every performance outside the U.S. Define variables for this problem. Answer: x = # of performances in the U.S. y = # of performances outside the U.S. Diff: 3 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: break-even analysis AACSB: Analytical thinking

48) A business analyst describes his company's profit function as 3x2 + 6x - 200. If x is the output volume, what statements can you make about the price, fixed cost, and variable cost? Answer: The fixed cost is $200, but we can't determine exactly what the price and variable cost are. Diff: 3 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis, variable definition AACSB: Analytical thinking

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49) A script writer has received an advance against royalties of $10,000. The royalty rate is $2 for every performance in the U.S., and $3 for every performance outside the U.S. Write an expression that could be used to compute the number of performances in order to cover the advance. Answer: 10000 = 2x + 3y Diff: 3 Page Ref: 5 Section Heading: The Management Science Approach to Problem Solving Keywords: break-even analysis AACSB: Analytical thinking

50) Students are organizing a "Battle of the Bands" contest. They know that at least 100 people will attend. The rental fee for the hall is $150 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? Answer: $6.50 Diff: 2 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

51) A popular performer is scheduled to appear at a major city. The promoter is deciding between two venues, the larger of which costs $20,000 to rent and the smaller of which costs $12,000 to rent. Ticket prices for the smaller venue are $20, but the promoter is unsure what to charge per ticket for the larger venue. If exactly 1000 customers arrive, what percentage change in ticket prices would make the profit at the large venue identical to that of the smaller venue? Answer: Increase 40% Diff: 3 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

52) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. Define variables that would tell how many units to purchase from each source. Answer: X1 = # of units from cooperative A X2 = # of units from cooperative B Diff: 3 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: break-even analysis, variable definition AACSB: Analytical thinking

53) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. Develop an objective function that would minimize the total cost. Answer: Min 6x1 + 5.5x2 Diff: 3 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function, break-even analysis, model development AACSB: Analytical thinking

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54) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. The manufacturer needs at least 12,000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. Develop constraints for these conditions. Answer: XA + XB ≥ 12000 XA ≤ 8000 XB ≥ 6000 Diff: 3 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints, model development AACSB: Analytical thinking

55) A group of professors struggles to craft a set of assessment questions for their operations management intro class. They want to cover four topic areas with at least four questions each and have no more than twenty questions total for the assessment. What would a set of constraints look like if they chose an optimization approach to the assessment? Answer: X1 ≥ 4 X2 ≥ 4 X3 ≥ 4 X4 ≥ 4 X1 + X2 + X3 + X4 ≤ 20 Diff: 3 Page Ref: 5 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints AACSB: Analytical thinking

56) What are some different types of decision support systems? Answer: A DSS can be small and singular, such as an Excel spreadsheet set up for a single user to solve a specific type of problem. A DSS can also be large and complex, linking many users and databases. The DSS can be a data-oriented system or a model-oriented system. Some decision support systems (ERP systems) help managers make decisions about all facets of a company's operations. Diff: 2 Page Ref: 21 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking

57) A manager of the cereal bar at the college campus has determined that the profit made for each bowl of Morning Buzz cereal sold, x, is equal to: Z = $4x - 0.5x. Each bowl of Morning Buzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day, which can be written as the constraint, 6x ≤ 192. What maximum profit will be made from Morning Buzz if it is all sold in one day? Answer: $112 Diff: 2 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: model development AACSB: Analytical thinking

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58) The College Coffee Cafe buys tea from three suppliers. The price per pound is $15.00 from supplier A, $17.50 from supplier B, and $21.00 from supplier C. They have budgeted $175 to purchase the tea. The cafe needs at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions. Answer: 15.00 XA + 17.50 XB + 21 XC ≤ 175 XA + XB + XC ≥ 12 XC ≤ 4 Diff: 3 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints, model development AACSB: Analytical thinking

59) The College Coffee Cafe receives a profit of $1.25 for each cup of house tea that they sell, $1.40 for each cup of the premium brand, and $1.50 for each cup of their special blend. Develop an objective that maximizes profit. Answer: Max 1.25x1 + 1.40x2 + 1.50x3 Diff: 2 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function, model development AACSB: Analytical thinking

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Yowzah Bids Yowzah receives bids from four companies we'll call A, B, C, and D to supply product for the coming year. Renee DeCartes, the Yowzah VP of Plotting takes the bids and creates this graph to bring to the next executive meeting.

60) Describe a general approach for determining the variable cost of any of the companies in this plot. Answer: The variable cost is reflected by the slope, so a rise over run formulation can be used. The leftmost edge of the graph represents x = 0 and the rightmost is a value of 20,000, which is a difference of 20,000. By subtracting the leftmost y-coordinate from each line from the rightmost, the rise can be computed. Then dividing the rise, or ∆y, by the run, ∆x, to determine the variable cost. Diff: 2 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

61) Which of the companies has the greatest variable cost? Answer: The variable cost is reflected by the slope, and the line representing company A starts lower than the others on the left side of the graph and ends higher than all others, thus it must have the greatest slope and therefore highest variable cost. Diff: 1 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

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62) What is the point of indifference between company A and company C? How does this point of indifference affect Yowzah's decision? Answer: Company A appears to have a fixed cost of 75,000 and company C appears to have a fixed cost of 160,000. The variable cost (slope) for company A is (375,000 - 75,000)/20,000 = 15. The variable cost (slope) for company C is (280,000 - 160,000)/20,000 = 6. The point of indifference can be found by setting the two lines equal to each other, so 75,000 + 15x = 160,000 + 6x; 9x = 85,000; x = 9444.4 The point of indifference doesn't affect Yowzah's decision in this range as both companies have higher costs than their fierce rival company B around this range of output. Diff: 1 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

63) The steps of the management science process are: A) problem definition, model construction, observation, model solution, implementation. B) observation, problem definition, model construction, model solution, implementation. C) model construction, problem definition, observation, model solution, implementation. D) observation, implementation, problem definition, model construction, model solution. Answer: B Diff: 1 Page Ref: 2 Section Heading: The Management Science Approach to Problem Solving Keywords: steps of sci method, prob solving approach, mgt sci process AACSB: Analytical thinking

64) A model is a functional relationship that includes: A) variables. B) parameters. C) equations. D) all of the above Answer: D Diff: 1 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: model AACSB: Analytical thinking

65) Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model? A) a decision variable B) an objective function C) a constraint D) a parameter Answer: C Diff: 2 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: model, constraint AACSB: Analytical thinking

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66) There is considerable overlap in the scientific method and management science techniques. Which of the following steps is shared between them? A) observation B) problem definition C) model construction D) implementation Answer: C Diff: 2 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: scientific approach AACSB: Analytical thinking

67) Which of the following is incorrect with respect to the use of models in decision making? A) They improve understanding of the problem. B) They promote subjectivity in decision making. C) They are generally easy to use. D) They provide a systematic approach to problem solving. Answer: B Diff: 3 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: model, problem solving AACSB: Analytical thinking

68) The field of management science: A) approaches decision making irrationally with techniques based on the scientific method. B) is another name for management or human resources management. C) concentrates on the use of quantitative methods to assist managers in decision making. D) is completely separate and distinct from all other disciplines. Answer: C Diff: 1 Page Ref: 2 Section Heading: The Management Science Approach to Problem Solving Keywords: management science, operations research AACSB: Analytical thinking

69) The processes of problem observation: A) cannot be done until alternatives are proposed. B) requires consideration of multiple criteria. C) is the first step of decision making. D) is the final step of problem solving. Answer: C Diff: 1 Page Ref: 2 Section Heading: The Management Science Approach to Problem Solving Keywords: observation, problem observation, management science process AACSB: Analytical thinking

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70) The limits of the problem and the degree to which it pervades other units in the organization must be included during the ________ step of the management science process. A) observation B) definition C) solution D) implementation Answer: B Diff: 1 Page Ref: 2 Section Heading: The Management Science Approach to Problem Solving Keywords: management science process AACSB: Analytical thinking

71) ________ involves determining the functional relationship between variables, parameters, and equations. A) Problem observation B) Problem definition C) Model construction D) Model solution Answer: C Diff: 1 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: management science process, model construction AACSB: Analytical thinking

72) Which steps of the management science process can either be a recommended decision or information that helps a manager make a decision? A) model implementation B) problem definition C) model solution D) problem formulation Answer: C Diff: 2 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: management science process, model solution AACSB: Analytical thinking

73) The result of an effective decision making process should be monitored in order to: A) reveal the break-even point. B) reveal errors in the implementation. C) keep fixed and variable costs distinct. D) change the scientific method. Answer: B Diff: 2 Page Ref: 7 Section Heading: The Management Science Approach to Problem Solving Keywords: decision making process AACSB: Analytical thinking

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74) Which of these disciplines typically does not fall under the umbrella of analytics? A) information systems B) statistics C) management science D) operations management Answer: D Diff: 2 Page Ref: 7 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge

75) The indicator that results in total revenues being equal to total cost is called the: A) marginal cost. B) marginal volume. C) break-even point. D) profit mix. Answer: C Diff: 1 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

76) Variable cost: A) depends on the number of units produced. B) plus marginal cost equals fixed cost. C) is equal to total cost in deterministic models. D) is the same as average cost. Answer: A Diff: 2 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

77) The components of break-even analysis are: A) cost and profit. B) volume and cost. C) volume, cost and profit. D) volume and profit. Answer: C Diff: 1 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

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78) ________ are generally independent of the volume of units produced and sold. A) Fixed costs B) Variable costs C) Profits D) Average cost Answer: A Diff: 1 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

79) The purpose of break-even analysis is to determine the number of units of a product to sell that will: A) appeal to the consumer. B) result in a profit. C) result in a loss. D) result in zero profit. Answer: D Diff: 2 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

80) Variable cost does not include: A) raw materials and resources. B) staff and management salaries. C) material handling and freight. D) direct labor and packaging. Answer: B Diff: 2 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

81) Which variable is not a component of break-even analysis? A) fixed costs B) variable costs C) number of employees D) number of customers Answer: C Diff: 1 Page Ref: 8 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

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82) At the break-even point: A) total revenue equals total cost. B) profit is maximized. C) revenue is maximized. D) costs are minimized. Answer: A Diff: 1 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

83) If the price increases, but fixed and variable costs do not change, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease, depending on sales. Answer: A Diff: 2 Page Ref: 11 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

84) If the price decreases, but fixed and variable costs do not change, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease, depending on sales. Answer: B Diff: 2 Page Ref: 11 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

85) The term ________ refers to testing how a problem solution reacts to changes in one or more of the model parameters. A) graphical solution B) decision analysis C) sensitivity analysis D) break-even analysis Answer: C Diff: 2 Page Ref: 11 Section Heading: Model Building: Break-Even Analysis Keywords: sensitivity analysis, modeling process AACSB: Analytical thinking

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86) If fixed costs decrease, but variable cost and price remain the same, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease depending on sales. Answer: A Diff: 2 Page Ref: 12 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

87) If fixed costs increase, but variable cost and price remain the same, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease depending on sales. Answer: B Diff: 2 Page Ref: 12 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

88) Administrators at a university will charge students $150 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even? A) 18 B) 20 C) 24 D) 30 Answer: C Diff: 2 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

89) A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? A) $120 B) $150 C) $175 D) $200 Answer: C Diff: 2 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

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90) A university is planning an online seminar. It costs $30 to live stream an instructor from Elbonia. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? A) $55 B) $15 C) $26.50 D) $75.75 Answer: C Diff: 2 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

91) It costs $50,000 to start a production process. Variable cost is $25 per unit and revenue is $45 per unit. What is the break-even point? A) 1000 units B) 1111 units C) 2000 units D) 2500 units Answer: D Diff: 1 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

92) It costs $6,000 to start a production process. Variable cost is $2 per unit and revenue is $5 per unit. What is the break-even point? A) 1000 units B) 1111 units C) 2000 units D) 2500 units Answer: C Diff: 1 Page Ref: 9 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

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93) The company with the lowest variable cost is: A) A. B) B. C) C. D) D. Answer: D Diff: 2 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

94) The company with the highest variable cost is: A) A. B) B. C) C. D) D. Answer: A Diff: 2 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

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95) Over the range of demand shown by this graph, which action would completely remove one of the potential suppliers from consideration? A) lowering A's fixed cost by 10% B) raising B's variable cost by 10% C) raising C's variable and fixed costs by 10% D) lowering D's fixed cost by 25% Answer: C Diff: 2 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

96) Which of these changes would have no effect on which supplier is chosen in the output range of 0 units to 20,000 units? A) Variable costs fall 10% for all bidders. B) Fixed costs rise 10% for all bidders. C) Companies A and B swap their figures for fixed costs. D) Companies C and D swap their figures for fixed costs. Answer: B Diff: 2 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

97) Which level of anticipated demand is least sensitive to variations in fixed and variable cost estimates? A) 5,000 B) 10,000 C) 15,000 D) 20,000 Answer: B Diff: 2 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

98) Company A has a fixed cost of 75,000 and a variable cost of 15. Company B's fixed cost is 90,000 and variable cost is 11. At what point is Yowzah indifferent between the two bidders? A) 3,250 B) 3,500 C) 3,750 D) 4,000 Answer: C Diff: 2 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

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99) Yowzah receives a frantic call from company C. Evidently the fixed cost they quoted was in rupees rather than dollars. If the current exchange rate is 60 rupees to the dollar, what is the net effect of an updated analysis? A) Company C is the bidder of choice throughout the range depicted in the graph. B) Company C has the highest total cost throughout the range depicted in the graph. C) Company C has the highest fixed cost of all four companies. D) Even beyond the range depicted in the graph, company C would be the bidder of choice. Answer: A Diff: 1 Page Ref: 10 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking

100) Which of the following statements is false? A) Decision models selectively describe the managerial situation. B) Decision models consider all factors from the real world. C) Decision models designate performance measures that reflect objectives. D) Decision models designate decision variables. Answer: B Diff: 2 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: models, decision models, modeling techniques AACSB: Analytical thinking

101) Decision support systems and sensitivity analysis are useful management science tools for answering the question: A) by when? B) who else? C) how much? D) what if? Answer: D Diff: 2 Page Ref: 21 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking

102) A difficult aspect of using spreadsheets to solve management science problems is: A) obtaining the solution to standard management science problems. B) data entry. C) performing sensitivity analysis. D) setting up a spreadsheet with complex models and formulas. Answer: D Diff: 2 Page Ref: 13 Section Heading: Computer Solution Keywords: computer solution, spreadsheets AACSB: Analytical thinking

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103) A technique that assumes certainty in its solution is referred to as: A) stochastic. B) probabilistic. C) deterministic. D) parametric. Answer: C Diff: 2 Page Ref: 17 Section Heading: Management Science Modeling Techniques Keywords: modeling, models, modeling techniques AACSB: Analytical thinking

104) Classification of management science techniques does not recognize: A) linear mathematical programming. B) probabilistic techniques. C) network techniques. D) computer programming. Answer: D Diff: 1 Page Ref: 16 Section Heading: Management Science Modeling Techniques Keywords: management science techniques, classification of techniques AACSB: Analytical thinking

105) Linear mathematical programming techniques assume that all parameters in the models are: A) known with certainty. B) unknown. C) predictable. D) unpredictable. Answer: A Diff: 2 Page Ref: 16 Section Heading: Management Science Modeling Techniques Keywords: management science techniques AACSB: Analytical thinking

106) Decision analysis is a ________ technique. A) linear mathematical programming B) probabilistic C) network D) non-linear programming technique Answer: B Diff: 1 Page Ref: 17 Section Heading: Management Science Modeling Techniques Keywords: management science techniques AACSB: Analytical thinking

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107) Which one of the following techniques is not a mathematical programming technique? A) linear programming models B) transportation models C) analytical hierarchy process D) integer linear programming technique Answer: C Diff: 2 Page Ref: 18 Section Heading: Management Science Modeling Techniques Keywords: management science techniques AACSB: Analytical thinking

108) Which one of the following management science methods is not a probabilistic technique? A) assignment models B) decision analysis C) queuing analysis D) statistical analysis Answer: A Diff: 2 Page Ref: 18 Section Heading: Management Science Modeling Techniques Keywords: management science techniques AACSB: Analytical thinking

109) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is: A) x1 ≤ 8, x2 ≤ 8, x3 ≤ 8. B) x1 + x2 + x3 ≥ 24. C) x1 + x2 + x3 ≤ 24. D) 4x1 + 3x2 + 2x3 ≤ 24. Answer: D Diff: 3 Page Ref: 16 Section Heading: Management Science Modeling Techniques Keywords: constraints AACSB: Analytical thinking

110) An objective function: A) shows where the break-even point is. B) describes how much of a resource can be used. C) can represent costs or profits. D) describes something to be maximized. Answer: C Diff: 2 Page Ref: 16 Section Heading: Management Science Modeling Techniques Keywords: objective function, model construction AACSB: Analytical thinking

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111) Larry's Fish Market buys salmon (S) for $5 per pound and a local whitefish (W) for $3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than $160. The objective function that minimizes these costs for Larry is: A) 5S + 3.5W ≤ 160. B) Min 5S + 3.5 W. C) Max 5S + 3.5 W. D) Min 5S + 3.5W ≥ 160. Answer: B Diff: 3 Page Ref: 3 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function, model construction AACSB: Analytical thinking

112) It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is an appropriate objective function for this scenario? A) Min Z = 1D + 0.5C B) Min Z = 2D + 1C C) Min Z = D + C ≤ 40 D) Min Z = D + C ≥ 3 Answer: A Diff: 3 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function AACSB: Analytical thinking

113) It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is one appropriate constraint for this scenario? A) 7C + 4D ≥ 3 B) 1C + 2D ≤ 40 C) .5C + 1D ≤ 40 D) 7C + 4D ≥ 1.5 Answer: C Diff: 3 Page Ref: 4 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints AACSB: Analytical thinking

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114) Marriott used which of the following management science techniques to help improve profit by $120 million over two years? A) optimization, decision analysis, and forecasting B) forecasting, queuing theory, and inventory analysis C) queuing theory, optimization, and inventory analysis D) forecasting, simulation, and optimization Answer: D Diff: 3 Page Ref: 6 Section Heading: The Management Science Approach to Problem Solving Keywords: management science, management scientist AACSB: Analytical thinking

115) Which of these decision support systems is the most comprehensive with respect to an entire organization? A) an Excel spreadsheet B) an ERP C) QM for Windows D) OLAP Answer: B Diff: 2 Page Ref: 21 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 2 Linear Programming: Model Formulation and Graphical Solution 1) Linear programming is a model consisting of linear relationships representing a firm's decisions given an objective and resource constraints. Answer: TRUE Diff: 2 Page Ref: 32 Section Heading: Model Formulation Keywords: model formulation AACSB: Analytical thinking

2) The objective function always consists of either maximizing or minimizing some value. Answer: TRUE Diff: 2 Page Ref: 32 Section Heading: Model Formulation Keywords: objective function AACSB: Analytical thinking

3) The objective function is a linear relationship reflecting the objective of an operation. Answer: TRUE Diff: 1 Page Ref: 32 Section Heading: Model Formulation Keywords: model formulation AACSB: Analytical thinking

4) A constraint is a linear relationship representing a restriction on decision making. Answer: TRUE Diff: 1 Page Ref: 32 Section Heading: Model Formulation Keywords: model formulation AACSB: Analytical thinking

5) Proportionality means the slope of a constraint is proportional to the slope of the objective function. Answer: FALSE Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models, proportionality AACSB: Analytical thinking

6) The terms in the objective function or constraints are additive. Answer: TRUE Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models, additive AACSB: Analytical thinking

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7) The terms in the objective function or constraints are multiplicative. Answer: FALSE Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models, additive AACSB: Analytical thinking

8) All linear programming models exhibit a set of constraints. Answer: TRUE Diff: 1 Page Ref: 32 Section Heading: Model Formulation Keywords: properties of linear programming models, constraints AACSB: Analytical thinking

9) When using the graphical method, only one of the four quadrants of an xy-axis needs to be drawn. Answer: TRUE Diff: 1 Page Ref: 37 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical linear programming AACSB: Analytical thinking

10) Linear programming models exhibit linearity among all constraint relationships and the objective function. Answer: TRUE Diff: 1 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear prog models, linearity, proportionality AACSB: Analytical thinking

11) The equation 8xy = 32 satisfies the proportionality property of linear programming. Answer: FALSE Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: graphical solution, proportionality AACSB: Analytical thinking

12) Typically, finding a corner point for the feasible region involves solving a set of three simultaneous equations. Answer: FALSE Diff: 2 Page Ref: 43 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, extreme points, feasible region AACSB: Analytical thinking

13) Objective functions in linear programs always minimize costs. Answer: FALSE Diff: 2 Page Ref: 32 Section Heading: Model Formulation Keywords: properties of linear programming models, objective function AACSB: Analytical thinking

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14) The feasible solution area contains infinite solutions to the linear program. Answer: TRUE Diff: 1 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: properties of linear programming models, feasible solution area AACSB: Analytical thinking

15) There is exactly one optimal solution point to a linear program. Answer: FALSE Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: properties of linear programming models, optimal solution pt AACSB: Analytical thinking

16) The following equation represents a resource constraint for a maximization problem: X + Y ≥ 20. Answer: FALSE Diff: 2 Page Ref: 34 Section Heading: A Maximization Model Example Keywords: properties of linear programming models, constraints AACSB: Analytical thinking

17) The optimal solution for a graphical linear programming problem is the corner point that is the farthest from the origin. Answer: FALSE Diff: 2 Page Ref: 40 Section Heading: Graphical Solutions of Linear Programming Models Keywords: feasibility, constraints AACSB: Analytical thinking

18) A minimization model of a linear program contains only surplus variables. Answer: FALSE Diff: 1 Page Ref: 53 Section Heading: A Minimization Model Example Keywords: properties of linear programming models, surplus variables AACSB: Analytical thinking

19) In the graphical approach, simultaneous equations may be used to solve for the optimal solution point. Answer: TRUE Diff: 2 Page Ref: 43 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking

20) Slack variables are only associated with maximization problems. Answer: FALSE Diff: 2 Page Ref: 45 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, slack variables AACSB: Analytical thinking

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21) Surplus variables are only associated with minimization problems. Answer: FALSE Diff: 2 Page Ref: 53 Section Heading: A Minimization Model Example Keywords: graphical solution, surplus variable AACSB: Analytical thinking

22) If the objective function is parallel to a constraint, the constraint is infeasible. Answer: FALSE Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solution AACSB: Analytical thinking

23) Multiple optimal solutions occur when constraints are parallel to each other. Answer: FALSE Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solution AACSB: Analytical thinking

24) Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Answer: TRUE Diff: 2 Page Ref: 40 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, objective function line AACSB: Analytical thinking

25) The first step in formulating a linear programming model is to define the objective function. Answer: FALSE Diff: 2 Page Ref: 32 Section Heading: Introduction Keywords: linear programming problems, formulation AACSB: Analytical thinking

26) A linear programming problem requires a choice between alternative courses of action. Answer: TRUE Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming problems, formulation AACSB: Application of knowledge

27) The term continuous is synonymous with divisible in the context of linear programming. Answer: TRUE Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming problems, formulation AACSB: Application of knowledge

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28) Linear programming problems can model decreasing marginal returns. Answer: FALSE Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming problems, formulation AACSB: Application of knowledge

29) ________ are mathematical symbols representing levels of activity. Answer: Decision variables Diff: 1 Page Ref: 32 Section Heading: Model Formulation Keywords: decision variables, model formulation AACSB: Analytical thinking

30) A ________ is a linear relationship representing a restriction on decision making. Answer: constraint Diff: 1 Page Ref: 32 Section Heading: Model Formulation Keywords: constraint, model formulation AACSB: Analytical thinking

31) If at least one constraint in a linear programming model is violated, the solution is said to be ________. Answer: infeasible Diff: 1 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: constraint, infeasible solution AACSB: Analytical thinking

32) A graphical solution is limited to solving linear programming problems with ________ decision variables. Answer: two Diff: 1 Page Ref: 36 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking

33) The ________ solution area is an area bounded by the constraint equations. Answer: feasible Diff: 1 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking

34) Multiple optimal solutions can occur when the objective function line is ________ to a constraint line. Answer: parallel Diff: 2 Page Ref: 45 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, multiple optimal solutions AACSB: Analytical thinking

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35) When a maximization problem is ________, the objective function can increase indefinitely without reaching a maximum value. Answer: unbounded Diff: 2 Page Ref: 56 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solution, unbounded problem AACSB: Analytical thinking

36) The best feasible solution is ________. Answer: optimal Diff: 1 Page Ref: 41 Section Heading: Graphical Solutions of Linear Programming Models Keywords: optimal solutions AACSB: Analytical thinking

37) In a constraint, the ________ variable represents unused resources. Answer: slack Diff: 1 Page Ref: 45 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, surplus variable AACSB: Analytical thinking

38) ________ is the difference between the left- and right-hand sides of a greater than or equal to constraint. Answer: Surplus Diff: 1 Page Ref: 53 Section Heading: A Minimization Model Example Keywords: surplus AACSB: Analytical thinking

39) If the objective function is parallel to a constraint, the linear program could have ________. Answer: multiple optimal solutions Diff: 2 Page Ref: 45 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solutions, multiple optimal solutions AACSB: Analytical thinking

40) Corner points on the boundary of the feasible solution area are called ________ points. Answer: extreme Diff: 1 Page Ref: 42 Section Heading: Graphical Solutions of Linear Programming Models Keywords: feasibility, constraints AACSB: Analytical thinking

41) ________ are at the endpoints of the constraint line segment that the objective function parallels. Answer: Alternate optimal solutions Diff: 3 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: alternative optimal solutions, multiple optimal solutions AACSB: Analytical thinking

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42) The ________ step in formulating a linear programming model is to define the decision variables. Answer: first Diff: 1 Page Ref: 34 Section Heading: A Maximization Model Example Keywords: linear programming, formulation AACSB: Analytical thinking

43) The management scientist constructed a linear program to help the alchemist maximize his gold production process. The computer model chugged away for a few minutes and returned an answer of infinite profit., which is what might be expected from a(n) ________ problem. Answer: unbounded Diff: 1 Page Ref: 56 Section Heading: Irregular Types of Linear Programming Problems Keywords: unbounded AACSB: Analytical thinking

44) The ________ property of linear programming models indicates that the rate of change, or slope, of the objective function or a constraint is constant. Answer: proportionality or linearity Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models, certainty AACSB: Analytical thinking

45) The objective function 3x + 2y + 4xy violates the assumption of ________. Answer: proportionality Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming properties AACSB: Application of knowledge

46) Mildred is attempting to prepare an optimal quantity of macaroni and cheese for the potluck supper this Sunday. The instructions indicate that one cup of water is needed for each box she needs to prepare. She sleeps well on Saturday night, secure in her knowledge that she knows the precise amount of water she will need the next day. This knowledge illustrates the assumption of ________. Answer: certainty Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming properties AACSB: Application of knowledge

47) Tim! airlines procurement division works with their linear programming algorithm to secure contracts for gasoline for the coming year. After twenty minutes of thinking, the computer suggests that they secure 425.8125 contracts with their suppliers. This value illustrates the assumption of ________ in linear programming models. Answer: divisibility or continuous Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming properties AACSB: Application of knowledge

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48) Solve the following graphically: Max z = 3x1 + 4x2 s.t.

x1 + 2x2 ≤ 16 2x1 + 3x2 ≤ 18 x1 ≥ 2 x2 ≤ 10 x1, x2 ≥ 0

What are the optimal values of x1, x2, and z? Answer: x1 = 9, x2 = 0, z = 27

Diff: 3 Page Ref: 37-41 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, simultaneous solution AACSB: Analytical thinking

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49) A novice business analyst develops the following model to determine the optimal combination of socks and underwear to take on his next business trip. The model is as follows: Maximize 5S+7U subject to: 3S - 2U≤ 45 7S + 3U≤ 33 2S + 8U≤ 70 Solve this problem graphically and determine how many of each item the analyst should pack. Answer: The optimal solution lies at the point representing 1.08 socks and 8.48 underwear. I suppose this is why I referred to the analyst as a novice.

Corner points and the objective function value in (Socks,Underwear) order are: Z(0,0)=0 Z(4.714,0)=23.57 Z(0,8.75)=61.25 Z(1.08. 8.48)=64.76 optimal Diff: 3 Page Ref: 37-41 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking

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50) Nathan enters the final exam period needing to pull off a miracle to pass his three toughest classes, Healthy Life Choices, Success Central, and Walking Fitness. Naturally he would also prefer to expend as little effort as possible doing so and as luck would have it, he knows a guy that can help optimize his time and GPA using the magic of management science. The model they develop is built around the notion of time spent studying and doing all the assignments he has neglected throughout the semester. The model is as follows, where S represents time spent studying (in minutes) and A represents time spent making up assignments (also in minutes). Maximize Z = 6S + 4A subject to: HLC 12S+10A ≥ 100 SC 6S + 8A ≥ 64 W 7S - 3A ≥ 36 Graphing was never one of Nathan's strengths, so it is up to you to develop a graphical solution to his problem and advise him on how much time should be invested in studying and how much time should be spent catching up on assignments. Answer: The two corner points meriting investigation are (in (Studying, Assignments) order) Z(10.67,0)=64 Z(6.48,3.13)=51.46 the optimal solution

So, 6 minutes of studying and 3 minutes of working on assignments was all that was required for my first born to successfully complete his first semester with something other than a 0.0 GPA. Sad, but true. Diff: 2 Page Ref: 51-52 Section Heading: A Minimization Model Example Keywords: graphical solution AACSB: Analytical thinking

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51) Consider the following linear program: MAX s.t.

Z = 60A + 50B 10A + 20B ≤ 200 8A + 5B ≤ 80 A≥2 B≥5

Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z. Answer: Solution shown below.

Diff: 2 Page Ref: 37-41 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical linear programming AACSB: Analytical thinking

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52) Consider the following linear program: MIN s.t.

Z = 60A + 50B 10A + 20B ≤ 200 8A + 5B ≤ 80 A≥2 B≥5

Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z. Answer: A = 2, B = 5, Z = 370

Diff: 2 Page Ref: 37-41 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical linear programming AACSB: Analytical thinking

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53) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.

If this is a maximization, which extreme point is the optimal solution? Answer: E Diff: 1 Page Ref: 42 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, extreme points, feasible region AACSB: Analytical thinking

54) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.

If this is a minimization, which extreme point is the optimal solution? Answer: A Diff: 2 Page Ref: 42 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, extreme points, feasible region AACSB: Analytical thinking

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55) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.

What would the be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Answer: -3/2 Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solution, multiple optimal solutions AACSB: Analytical thinking

56) Consider the following linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0 Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint? Answer: x = 0, y = 8, revenue = $160, s1= 0 Diff: 2 Page Ref: 46 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, slack variables AACSB: Analytical thinking

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57) Given this model Maximize Z = 6S + 4A subject to: 12S + 10A ≥ 100 6S + 8A ≥ 64 7S - 3A ≥ 36 What is the optimal solution and the surplus associated with the first constraint? Answer: The optimal solution lies at S = 6.48 and A = 3.13. The s1 variable is 9.1892 Diff: 2 Page Ref: 52 Section Heading: A Minimization Model Example Keywords: surplus AACSB: Analytical thinking

58) The poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities. A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron. Formulate the linear programming model for this situation. Answer: Min Z = $4005C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Diff: 3 Page Ref: 34-35 Section Heading: A Maximization Model Example Keywords: constraint, model formulation AACSB: Analytical thinking

59) Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution? Answer: 9.25 at x1 = 0 and x2 = 4.625 Diff: 3 Page Ref: 42 Section Heading: Graphical Solutions of Linear Programming Models Keywords: minimization problem AACSB: Analytical thinking

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60) Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution? Answer: 9.25 at x1 = 0 and x2 = 4.625 Diff: 3 Page Ref: 42 Section Heading: Graphical Solutions of Linear Programming Models Keywords: minimization problem AACSB: Analytical thinking

61) Ponder the following linear programming problem: MIN Z = 3x1 + 8x2 Subject to: 3x1 + 4x2 ≥ 52 3x1 + 4x2 ≥ 38 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution? Answer: 52 at x1 = 17.33 and x2 = 0.0 Diff: 3 Page Ref: 42 Section Heading: Graphical Solutions of Linear Programming Models Keywords: minimization problem AACSB: Analytical thinking

62) The international man of mystery knew the finest haberdashers the world over and constantly sought to expand his dazzling array of fine suits, ties, and cufflinks. Closet space was at a premium however, so purchases were carefully weighed. Each suit provides 23 units of dazzlement, each tie 14, and a set of cufflinks is worth an easy 8. A suit takes up 0.5 cubic feet of closet space and $900 of budget. A tie costs $135 and cufflinks cost $100 per set. Cufflinks are tiny — even in the original box, they take up only .01 cubic feet while ties occupy a lusty .25 cubic feet. He has budgeted $12,000 for clothes on this trip and has 20 cubic feet of closet space left to fill. Formulate an objective function and constraints to model this situation. Answer: Max Dazzlement = 23S + 14T + 8C subject to: 900S + 135T + 100C ≤ 12,000 0.5S + 0.25T + 0.01C ≤ 20 Diff: 3 Page Ref: 34 Section Heading: A Maximization Model Example Keywords: linear programming formulation AACSB: Analytical thinking

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63) Ponder the following linear programming problem: Max Z = 5x1 + 6x2 Subject to: 3x1 + 4x2 ≤ 76 8x1 + 9x2 ≤ 123 3x1 + 3x2 ≤ 56 x1, x2 ≥ 0 What is the optimal solution point? Answer: 12.31 at x1 and 2.72 at x2 for an objective function value of 77.897 Diff: 3 Page Ref: 40 Section Heading: A Maximization Model Example Keywords: optimal solutions AACSB: Analytical thinking

64) List the four properties of linear programming models and provide an example of a violation of each. Answer: Properties and brief discussions are contained in the table. Counter examples will vary. Proportionality The slope of a constraint or objective function is constant. There are no increasing or decreasing marginal returns on either. Additivity Strictly linear functions - there are no interaction effects among decision variables. Divisibility Non-integer values of decision variables are OK. Certainty All model parameters are known exactly. Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming properties AACSB: Application of knowledge

65) Formulate all elements of linear program to model your university effort. Include a narrative that explains each of the components. Answer: Answers will vary, perhaps dramatically. A noble objective function would seek to maximize a GPA or minimize total cost. Constraints would likely include budget, hours in a day, financial capital, conflicts with social endeavors, and others. Diff: 2 Page Ref: 32 Section Heading: Model Formulation Keywords: linear programming properties AACSB: Application of knowledge

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66) Consider the following linear programming problem: MIN Z = 10x1 + 20x2 Subject to: x1 + x2 ≥ 12 2x1 + 5x2 ≥ 40 x2 ≤ 13 x1, x2 ≥ 0 At the optimal solution, what is the value of surplus associated with constraint 1 and constraint 3, respectively? Answer: constraint 1: (0 surplus), constraint 2: (7.667 surplus) Diff: 2 Page Ref: 50-54 Section Heading: A Minimization Model Example Keywords: graphical solution AACSB: Analytical thinking

67) Given this set of constraints, for what objective function is the point x=5, y=3 in the feasible region? s.t 3x + 6y ≤ 30 10x + 10y ≤ 60 10x + 15y ≤ 90 Answer: No objective function can move that point into the feasible region. Diff: 2 Page Ref: 40 Section Heading: Graphical Solutions of Linear Programming Models Keywords: feasibility, constraints AACSB: Analytical thinking

68) Consider the following linear programming problem: MIN Z = 2x1 + 3x2 Subject to: x1 + 2x2 ≤ 20 5x1 + x2 ≤ 40 4x1 + 6x2 ≤ 60 x1 , x2 ≥ 0 What is the optimal solution? Answer: Multiple optimal solutions exist between the extreme point (0,10) and (6.92,5.38) along the line with a slope of -2/3. Diff: 2 Page Ref: 50-51 Section Heading: A Minimization Model Example Keywords: graphical solution, multiple optimal solutions AACSB: Analytical thinking

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69) A company producing a standard line and a deluxe line of dishwashers has the following time requirements (in minutes) in departments where either model can be processed. Standard Stamping Motor installation Wiring

3 10 10

Deluxe 6 10 15

The standard models contribute $20 each and the deluxe $30 each to profits. Because the company produces other items that share resources used to make the dishwashers, the stamping machine is available only 30 minutes per hour, on average. The motor installation production line has 60 minutes available each hour. There are two lines for wiring, so the time availability is 90 minutes per hour. Let

x = number of standard dishwashers produced per hour y = number of deluxe dishwashers produced per hour

Write the formulation for this linear program. Answer: Max 20x + 30y s.t 3x + 6y ≤ 30 10x + 10y ≤ 60 10x + 15y ≤ 90 Diff: 2 Page Ref: 34-35 Section Heading: A Maximization Model Example Keywords: formulation, objective function, constraints AACSB: Analytical thinking

70) In a linear programming problem, the binding constraints for the optimal solution are: 5x1 + 3x2 ≤ 30 2x1 + 5x2 ≤ 20 As long as the slope of the objective function stays between ________ and ________, the current optimal solution point will remain optimal. Answer: -5/3, -2/5 Diff: 3 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: optimal solution, solution interpretation, slope AACSB: Analytical thinking

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71) In a linear programming problem, the binding constraints for the optimal solution are: 5x1 + 3x2 ≤ 30 2x1 + 5x2 ≤ 20 Which of these objective functions will lead to the same optimal solution? A) 2x1 + 1x2 B) 7x1 + 8x2 C) 80x1 + 60x2 D) 25x1 + 15x2 Answer: D Diff: 3 Page Ref: 40 Section Heading: Graphical Solutions of Linear Programming Models Keywords: optimal solution, solution interpretation, slope AACSB: Analytical thinking

72) Decision variables: A) measure the objective function. B) measure how much or how many items to produce, purchase, hire, etc. C) always exist for each constraint. D) measure the values of each constraint. Answer: B Diff: 2 Page Ref: 32 Section Heading: Model Formulation Keywords: decision variables AACSB: Analytical thinking

73) In a linear programming problem, a valid objective function can be represented as: A) Max Z = 5xy B) Max Z 5x2 + 2y2 C) Max 3x + 3y + 1/3 z D) Min (x1 + x2) / x3 Answer: C Diff: 3 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: objective function AACSB: Analytical thinking

74) Which of the following could not be a linear programming problem constraint? A) 1A + 2B ≠ 3 B) 1A + 2B = 3 C) 1A + 2B ≤ 3 D) 1A + 2B ≥ 3 Answer: A Diff: 2 Page Ref: 34-35 Section Heading: A Maximization Model Example Keywords: formulation, constraints AACSB: Analytical thinking

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75) Which of the following could be a linear programming objective function? A) Z = 1A + 2BC + 3D B) Z = 1A + 2B + 3C + 4D C) Z = 1A + 2B / C + 3D D) Z = 1A + 2B2 + 3D Answer: B Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: objective function AACSB: Analytical thinking

76) The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the objective function? A) MAX $2R + $4D B) MAX $3R + $2D C) MAX $3D + $2R D) MAX $4D + $2R Answer: B Diff: 2 Page Ref: 34 Section Heading: A Maximization Model Example Keywords: formulation, objective function AACSB: Analytical thinking

77) The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint? A) 2D + 4R ≤ 480 B) 2R + 3D ≤ 480 C) 3R + 2D ≤ 480 D) 2R + 4D ≤ 480 Answer: D Diff: 2 Page Ref: 34-35 Section Heading: A Maximization Model Example Keywords: formulation, constraints AACSB: Analytical thinking

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78) The ________ property of linear programming models indicates that the rate of change or slope of the objective function or a constraint is constant. A) additive B) divisibility C) certainty D) proportionality Answer: D Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models AACSB: Analytical thinking

79) The ________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant. A) additive B) divisibility C) certainty D) proportionality Answer: C Diff: 2 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models AACSB: Analytical thinking

80) The region that satisfies all of the constraints in a graphical linear programming problem is called the: A) region of optimality. B) feasible solution space. C) region of non-negativity. D) optimal solution space. Answer: B Diff: 1 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasibility AACSB: Analytical thinking

81) In the formulation of a ≥ constraint: A) a surplus variable is subtracted. B) a surplus variable is added. C) a slack variable is subtracted. D) a slack variable is added. Answer: A Diff: 1 Page Ref: 53 Section Heading: A Minimization Model Example Keywords: surplus AACSB: Analytical thinking

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82) Which of the following statements is not true? A) An infeasible solution violates all constraints. B) A feasible solution point does not have to lie on the boundary of the feasible solution. C) A feasible solution satisfies all constraints. D) An optimal solution satisfies all constraints. Answer: A Diff: 2 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasibility AACSB: Analytical thinking

83) A hot dog manufacturer wishes to minimize the cost in dollars of producing a low-cost niched product while meeting the dietary guidelines for protein and sodium. Once the model has been run, the surplus variable in the sodium constraint has a value of 1300 milligrams. The best interpretation of this outcome is: A) The value of the sodium in a hot dog is 1300. B) The amount of sodium in a single hot dog should be 1300 milligrams. C) The minimum cost hot dog has 1300 milligrams more sodium than required. D) A hot dog should have at least 1300 milligrams of sodium. Answer: C Diff: 2 Page Ref: 53 Section Heading: A Minimization Model Example Keywords: surplus AACSB: Analytical thinking

84) Which of these statements is best? A) An unbounded problem is also infeasible. B) An infeasible problem is also unbounded. C) An unbounded problem has feasible solutions. D) An infeasible problem has unbounded solutions. Answer: C Diff: 2 Page Ref: 56 Section Heading: Irregular Types of Linear Programming Problems Keywords: infeasible problem, infeasible solution AACSB: Analytical thinking

85) The optimal solution to a linear programming model that has been solved using the graphical approach: A) is typically located at the origin. B) must be below and on the left side of all constraint lines. C) must be above and the right of all constraint lines. D) is typically at some corner of the feasible region. Answer: D Diff: 1 Page Ref: 40 Section Heading: Graphical Solutions of Linear Programming Models Keywords: solution AACSB: Analytical thinking

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86) Without satisfying the non-negativity constraint, a solution that satisfies all the other constraints of a linear programming problem is called: A) feasible. B) infeasible. C) semi-feasible. D) optimal. Answer: B Diff: 3 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasibility AACSB: Analytical thinking

87) An intern sets up a linear program to optimize the use of paper products in the men's washroom. The system of equations he develops is: Max 2T + 3S + 4ST s.t 3T + 6S ≤ 40 10T + 10S ≤ 66 10T + 15S ≤ 99 His mentor studies the model, frowns, and admonishes the intern for violating which of the following properties of linear programming models? A) divisibility B) proportionality C) certainty D) additivity Answer: D Diff: 1 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: additivity AACSB: Analytical thinking

88) Which of the following is not a typical characteristic of a linear programming problem? A) Restrictions exist. B) A choice among alternatives is required. C) The problem can be solved graphically. D) The problem has an objective. Answer: C Diff: 1 Page Ref: 57 Section Heading: Characteristics of Linear Programming Problems Keywords: graphical solution AACSB: Analytical thinking

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89) The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. Which of the following is not a feasible production combination? A) 90R and 75D B) 135R and 0D C) 75R and 90D D) 40R and 100D Answer: C Diff: 3 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasibility AACSB: Analytical thinking

90) The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit? A) R = 75, D = 90, Z = $405 B) R = 135, D = 0, Z = $405 C) R = 90, D = 75, Z = $420 D) R = 40, D= 100, Z = $320 Answer: C Diff: 3 Page Ref: 42 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking

91) ________ is used to analyze changes in model parameters. A) Optimal solution B) Feasible solution C) Sensitivity analysis D) A slack variable Answer: C Diff: 2 Page Ref: 45 Section Heading: Graphical Solutions of Linear Programming Models Keywords: sensitivity analysis AACSB: Analytical thinking

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92) Cully Furniture buys two products for resale: big shelves (B)and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. Which of the following is not a feasible purchase combination? A) 100 big shelves and 82 medium shelves B) 150 big shelves and 0 medium shelves C) 100 big shelves and 100 medium shelves D) 100 big shelves and 0 medium shelves Answer: C Diff: 3 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: formulation, feasibility AACSB: Analytical thinking

93) Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit? A) $35,000 B) $45,000 C) $55,000 D) $65,000 Answer: B Diff: 3 Page Ref: 41 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking

94) Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased? A) B = 90, M = 75 B) B = 150, M = 0 C) B = 0, M = 200 D) B = 100, M = 100 Answer: B Diff: 3 Page Ref: 41 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking

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95) The theoretical limit on the number of constraints that can be handled by a linear programming problem is: A) 2. B) 3. C) 4. D) unlimited. Answer: D Diff: 1 Page Ref: 32 Section Heading: Model Formulation Keywords: constraints AACSB: Analytical thinking

96) Consider the following maximization problem. MAX z = x + 2y s.t. 2x + 3y ≤ 6 5x + 6y ≤ 30 y≥1 The optimal solution: A) occurs where x = 4.67 and y = 1.11. B) occurs where x = 0 and y = 2. C) occurs where x = 6 and y = 0. D) results in an objective function value of 12. Answer: B Diff: 1 Page Ref: 42 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, extreme points, feasible region AACSB: Analytical thinking

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The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

97) This linear programming problem is a(n): A) maximization problem. B) minimization problem. C) irregular problem. D) cannot tell from the information given Answer: B Diff: 1 Page Ref: 50 Section Heading: A Minimization Model Example Keywords: graphical solution AACSB: Analytical thinking

98) The equation for constraint DH is: A) 4X + 8Y ≥ 32. B) 8X + 4Y ≥ 32. C) X + 2Y ≥ 8. D) 2X + Y ≥ 8. Answer: C Diff: 3 Page Ref: 50 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking

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99) Which of the following points is not feasible? A) A B) B C) H D) G Answer: D Diff: 1 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasible point AACSB: Analytical thinking

100) Which line is represented by the equation 2X + Y ≥ 8? A) BF B) CG C) DH D) AJ Answer: A Diff: 2 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, constraints AACSB: Analytical thinking

101) Which of the following constraints has a surplus greater than 0? A) BF B) CG C) DH D) AJ Answer: C Diff: 2 Page Ref: 53-54 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking

102) The constraint AJ: A) is a binding constraint. B) has no surplus. C) does not contain feasible points. D) contains the optimal solution. Answer: B Diff: 3 Page Ref: 53-54 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking

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Figure 2

103) Consider the optimization problem represented by this graph. Which of the following statements is best? A) This is a maximization problem with a feasible solution. B) This is a maximization problem with no feasible solution. C) This is a minimization problem with a feasible solution. D) This is a minimization problem with no feasible solution. Answer: C Diff: 1 Page Ref: 54 Section Heading: A Minimization Model Example Keywords: graphical solution, feasibility AACSB: Analytical thinking

104) Line segment GH represents the objective function. Which constraint has surplus? A) AB B) CD C) EF D) none of the constraints has surplus Answer: A Diff: 2 Page Ref: 53 Section Heading: A Minimization Model Example Keywords: graphical solution, surplus variable AACSB: Analytical thinking

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105) What is the equation for the constraint AB? A) 3X + 12Y ≥ 15 B) X + 4Y ≥ 12 C) X + Y ≥ 15 D) 12X +3Y ≥ 36 Answer: D Diff: 3 Page Ref: 51 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking

106) What is the equation for constraint EF? A) 4X + 8Y ≥ 64 B) 4X + 8Y ≥ 12 C) 16X + 8Y ≥ 24 D) 16X + 8Y ≥ 32 Answer: A Diff: 3 Page Ref: 51 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking

107) Consider the optimization problem represented by this graph. The objective function is represented by line GH. Where is the optimal solution? A) the intersection of lines AB and EF B) the intersection of lines AB and CD C) the intersection of lines CD and EF D) the upper right corner of the shaded region Answer: C Diff: 1 Page Ref: 51 Section Heading: A Minimization Model Example Keywords: graphical solution, objective function line AACSB: Analytical thinking

108) Consider the optimization problem represented by this graph. Line GH represents the objective function. Which of the following statements is best? A) This is a single optimal solution. B) All points along GH are optimal. C) All points on lines AB, CD and DE that touch the shaded region are optimal. D) All points in the shaded region are optimal Answer: A Diff: 1 Page Ref: 51 Section Heading: A Minimization Model Example Keywords: graphical solution, multiple optimal solutions AACSB: Analytical thinking

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109) In order for an optimization problem to have multiple optimal solutions: A) the objective function and one constraint must have the same y-intercept. B) the objective function and one constraint must have the same slope. C) two or more of the constraints must not have intersection points. D) two or more of the constraints must have the same slope. Answer: B Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solutions, multiple optimal solutions AACSB: Analytical thinking

110) An optimization problem that has multiple optimal solutions: A) means that there are actually no optimal solutions. B) is reflected by the entire feasible region being optimal C) means that the surplus for a third constraint cannot be calculated. D) provides the decision-maker with increased flexibility. Answer: D Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solutions, multiple optimal solutions AACSB: Analytical thinking

111) How would multiple optimal solutions typically appear on a graphical solution? A) a point B) a line C) a plane D) a cube Answer: B Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solutions, multiple optimal solutions AACSB: Analytical thinking

112) Which of the following statements about infeasible problems is best? A) All of the possible solutions violate at least one constraint. B) All of the possible solutions violate all of the constraints. C) At least one of the possible solutions violates all of the constraints. D) At least one of the possible solutions violates at least one of the constraints. Answer: A Diff: 1 Page Ref: 56 Section Heading: Irregular Types of Linear Programming Problems Keywords: infeasible problem, infeasible solution AACSB: Analytical thinking

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113) Greg, a young entrepreneur, has developed an aggressive business plan and is presenting his profit projections on the popular show Shark Tank in hopes of securing some venture capital. He concludes his presentation with an LP model of his planned product mix, and is convinced he will seal the deal by demonstrating that his profits are limitless since his LP model is unbounded. What should the sharks tell him? A) "Limitless profits sound fantastic, here's a blank check." B) "Limitless profits are possible only in minimization models, and we want you to maximize profits." C) "Unlimited profits aren't possible. You must have made a mistake in your LP model." D) "Limitless profits are possible only in maximization models, and we want you to minimize profits." Answer: C Diff: 1 Page Ref: 56 Section Heading: Irregular Types of Linear Programming Problems Keywords: unbounded AACSB: Analytical thinking

114) Multiple optimal solutions can occur when the objective function is ________ a constraint line. A) unequal to B) equal to C) perpendicular to D) parallel to Answer: D Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: irregular types of linear programming problems AACSB: Analytical thinking

115) A slack variable: A) is the amount by which the left side of a ≥ constraint is larger than the right side. B) is the amount by which the left side of a ≤ constraint is smaller than the right side. C) is the difference between the left and right side of a constraint. D) exists for each variable in a linear programming problem. Answer: B Diff: 2 Page Ref: 44 Section Heading: Slack Variables Keywords: slack variables AACSB: Analytical thinking

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116) The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used? A) only time B) only syrup C) time and syrup D) neither time nor syrup Answer: A Diff: 2 Page Ref: 46 Section Heading: Graphical Solutions of Linear Programming Models Keywords: slack variables AACSB: Analytical thinking

117) Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. If the furniture company purchases no big shelves and 200 medium shelves, which of the two resources will be completely used (at capacity)? A) investment money only B) storage space only C) investment money and storage space D) neither investment money nor storage space Answer: B Diff: 2 Page Ref: 39 Section Heading: Graphical Solutions of Linear Programming Models Keywords: slack variables AACSB: Analytical thinking

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118) Consider the following linear program: MAX z = 5x + 3y s.t. x-y≤6 x ≤1 The optimal solution: A) is infeasible. B) occurs where x = 1 and y = 0. C) occurs where x = 0 and y = 1. D) results in an objective function value of 5. Answer: D Diff: 2 Page Ref: 40 Section Heading: Graphical Solutions of Linear Programming Models Keywords: slack variables AACSB: Analytical thinking

119) The first step in solving a graphical linear programming model is to: A) plot the model constraints as equations on the graph and indicate the feasible solution area. B) plot the objective function and move this line out from the origin to locate the optimal solution point. C) solve simultaneous equations at each corner point to find the solution values at each point. D) determine which constraints are binding. Answer: A Diff: 1 Page Ref: 37 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphic solution, steps for solving a graphical linear prog model AACSB: Analytical thinking

120) The optimal solution of a minimization problem is at the extreme point ________ the origin. A) farthest from B) closest to C) exactly at D) parallel to Answer: B Diff: 2 Page Ref: 51 Section Heading: A Minimization Model Example Keywords: minimization problem AACSB: Analytical thinking

121) Multiple optimal solutions provide ________ flexibility to the decision maker. A) greater B) less C) greater or equal D) less or equal Answer: A Diff: 2 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: irregular types of linear programming problems AACSB: Analytical thinking

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122) Which of the following special cases does not require reformulation of the problem in order to obtain a solution? A) unboundedness B) infeasibility C) alternate optimality D) Each one of these cases requires reformulation. Answer: C Diff: 3 Page Ref: 55 Section Heading: Irregular Types of Linear Programming Problems Keywords: irregular types of linear programming problems AACSB: Analytical thinking

123) If the feasible region for a linear programming problem is unbounded, then the solution to the corresponding linear programming problem is ________ unbounded. A) always B) sometimes C) never D) There is not enough information to complete this statement. Answer: B Diff: 3 Page Ref: 56 Section Heading: Irregular Types of Linear Programming Problems Keywords: irregular types of linear programming problems, unboundedness AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 3 Linear Programming: Computer Solution and Sensitivity Analysis 1) The shadow price for a positive decision variable is 0. Answer: TRUE Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: shadow price, sensitivity analysis AACSB: Analytical thinking

2) When the right-hand sides of two constraints are both increased by one unit, the value of the objective function will be adjusted by the sum of the constraints' prices. Answer: FALSE Diff: 3 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitive analysis, right-hand-side AACSB: Analytical thinking

3) Most computer linear programming packages readily accept constraints entered in fractional form, such as X1/X3. Answer: FALSE Diff: 1 Page Ref: 78 Section Heading: Computer Solution Keywords: computer solution, formulation, constraint AACSB: Analytical thinking

4) Sensitivity ranges can be computed only for the right-hand sides of constraints. Answer: FALSE Diff: 1 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: computer solution AACSB: Analytical thinking

5) The marginal value of any scarce resource is the dollar amount one should be willing to pay for one additional unit of that scarce resource. Answer: TRUE Diff: 1 Page Ref: 80 Section Heading: Computer Solution Keywords: marginal value AACSB: Analytical thinking

6) Sensitivity analysis determines how a change in a parameter affects the optimal solution. Answer: TRUE Diff: 2 Page Ref: 82 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

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7) The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal. Answer: TRUE Diff: 2 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking

8) The sensitivity range for an objective function coefficient is the range of values over which the profit does not change. Answer: FALSE Diff: 2 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking

9) The sensitivity range for a constraint quantity value is the range over which the shadow price is valid. Answer: TRUE Diff: 2 Page Ref: 85 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking

10) If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change. Answer: TRUE Diff: 2 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking

11) The sensitivity range for a constraint quantity value is the range over which the optimal values of the decision variables do not change. Answer: FALSE Diff: 2 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking

12) Sensitivity analysis allows the modeler to relax the certainty assumption. Answer: TRUE Diff: 2 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, parameter changes AACSB: Application of knowledge

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13) The terms shadow price and dual price mean the same thing. Answer: TRUE Diff: 1 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

14) Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once. Answer: FALSE Diff: 2 Page Ref: 91 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

15) For a profit maximization problem, if the allowable increase for a coefficient in the objective function is infinite, then profits are unbounded. Answer: FALSE Diff: 2 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

16) The reduced cost (shadow price) for a positive decision variable is ________. Answer: zero Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking

17) ________ is the analysis of the effect of parameter changes on the optimal solution. Answer: Sensitivity analysis Diff: 2 Page Ref: 82 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

18) The sensitivity range for a constraint quantity value is also the range over which the ________ is valid. Answer: shadow price Diff: 2 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking

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19) The sensitivity range for a(n) ________ coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal. Answer: objective function Diff: 1 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking

Consider the following linear program, which maximizes profit for two products--regular (R) and super (S): MAX 50R + 75S s.t. 1.2 R + 1.6 S ≤ 600 assembly (hours) 0.8 R + 0.5 S ≤ 300 paint (hours) .16 R + 0.4 S ≤ 100 inspection (hours) Sensitivity Report:

Cell

Name

Final Value

$B$7 $C$7

Regular = Super =

291.67 133.33

0.00 0.00

50 75

70 50

20 43.75

Cell

Name

Final Value

Shadow Price

Constraint R.H. Side

Allowable Increase

Allowable Decrease

600 300 100

1E+30 39.29 12.94

36.67 175 40

$E$3 Assembly (hr/unit) $E$4 Paint (hr/unit) $E$5 Inspect (hr/unit)

Reduced Cost

Objective Coefficient

Allowable Increase

Allowable Decrease

563.33 300.00 100.00

0.00 33.33 145.83

20) The optimal number of regular products to produce is ________, and the optimal number of super products to produce is ________, for total profits of ________. Answer: 291.67, 133.33, $24,583 Diff: 1 Page Ref: 78 Section Heading: Computer Solution Keywords: computer solution AACSB: Analytical thinking

21) If the company wanted to increase the available hours for one of their constraints (assembly, painting, or inspection) by two hours, they should increase ________. Answer: inspection Diff: 2 Page Ref: 85 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

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22) The profit on the super product could increase by ________ without affecting the product mix. Answer: $50 Diff: 1 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: computer solution AACSB: Analytical thinking

23) If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by ________. Answer: $1,333 Diff: 2 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

24) A change in the market has increased the profit on the super product by $5. Total profit will increase by ________. Answer: $667 Diff: 2 Page Ref: 85 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. Max R = 14Z + 13Y + 17X subject to: Beef 2Z + 3Y + 4X ≤ 28 Cheese 9Z + 8Y + 11X ≤ 80 Beans 4Z + 4Y + 2X ≤ 68 X,Y,Z ≥ 0

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The sensitivity report from the computer model reads as follows:

25) Taco Loco should try to purchase additional ________, but should not buy more ________. Answer: beef and cheese, beans Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: shadow price, sensitivity analysis AACSB: Analytical thinking

26) Taco Loco should produce both ________ but should not make any ________. Answer: Z and Y, X Diff: 1 Page Ref: 78 Section Heading: Computer Solution Keywords: computer solution, spreadsheets AACSB: Analytical thinking

27) Taco Loco will make the same quantity of X, Y, and Z if the amount of cheese at their disposal is between ________ pounds and ________ pounds. Answer: 74.67, 126 Diff: 2 Page Ref: 88 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking

28) For humanitarian reasons, Taco Loco decides they would rather make product X than product Y. The dollar amount that they can both increase the price of Y and reduce the price of X by to accomplish this reversal of demand is ________. Answer: 82 cents (81.8 cents) Diff: 2 Page Ref: 81 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, parameter changes AACSB: Analytical thinking

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29) If Taco Loco reduces the price of the X product by about 82 cents, then their optimal product mix will contain ________ X. Answer: 0 units (none) Diff: 1 Page Ref: 91 Section Heading: Sensitivity Analysis Keywords: reduced cost AACSB: Analytical thinking

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

Formulation: Let x = number of tractors produced per period y = number of lawn mowers produced per period MAX 30x + 30y subject to 2x + y ≤ 60 2x + 3y ≤ 120 x ≤ 45 The graphical solution is shown below.

30) How many tractors and saws should be produced to maximize profit, and how much profit will they make? Answer: 15 tractors and 30 saws for $1350 in profit Diff: 2 Page Ref: 78 Section Heading: Computer Solution Keywords: graphical solution, simultaneous solution AACSB: Analytical thinking

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31) Determine the sensitivity range for the profit for tractors. Answer: 20 ≤ x ≤ 60 Diff: 2 Page Ref: 86 Section Heading: Sensitivity Analysis Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking

32) What is the shadow price for assembly? Answer: 0 Diff: 1 Page Ref: 86-90 Section Heading: Sensitivity Analysis Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking

33) What is the shadow price for fabrication? Answer: $7.50 Diff: 2 Page Ref: 84 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking

34) What is the maximum amount a manager would be willing to pay for one additional hour of machining time? Answer: $1357.50 - $1350 = $7.50 Diff: 3 Page Ref: 84 Section Heading: Sensitivity Analysis and Graphical Solution Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking

35) A breakdown in fabrication causes the available hours to drop from 120 to 90 hours. How will this impact the optimal number of tractors and mowers produced? Answer: x = 22.5, y = 15, Z = 1125, so profits will fall by $1350 - $1125 = $225. Students may also answer the question by determining the sensitivity range, which is from 60 to 180 hours, resulting in a profit change of 30 × $7.5 = $225. Diff: 3 Page Ref: 84 Section Heading: Sensitivity Analysis and Graphical Solution Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking

36) What is the range for the shadow price for assembly? Answer: allowable decrease = 45 - 15 = 30, and allowable increase is ∞. Diff: 2 Page Ref: 86 Section Heading: Sensitivity Analysis and Graphical Solution Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking

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The linear programming problem whose output follows is used to determine how many bottles of red nail polish (x1), blue nail polish (x2), green nail polish (x3), and pink nail polish (x4) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Note that green nail polish does not require any time to prepare its display. Constraints 3 and 4 are marketing restrictions. Constraint 3 indicates that the maximum demand for red and green polish is 25 bottles, while constraint 4 specifies that the minimum demand for blue, green, and pink nail polish bottles combined is at least 50 bottles. MAX 100x1 + 120x2 + 150x3 + 125x4 Subject to

x1 + 2x2 + 2x3 + 2x4 ≤ 108

3x1 + 5x2 + x4 ≤ 120

x1 + x3 ≤ 25

x2 + x3 + x4 ≥ 50 x1, x2 , x3, x4 ≥ 0

Optimal Solution: Objective Function Value = 7475.000

Variable x1

Value 8

Reduced Costs 0

Objective Coefficient Ranges Lower Variable Limit x1 87.5 x2

Current Value 100

Upper Limit 125

none

120

125

150

162

120

125

150

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Right Hand Side Ranges

37) How much space will be left unused? How many minutes of idle time remain for setting up the display? Answer: 0, 63 Diff: 3 Page Ref: 88 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

38) a) To what value can the per bottle profit on red nail polish drop before the solution (product mix) would change? b) By how much can the per bottle profit on green nail polish increase before the solution (product mix) would change? Answer: a) 87.5 b) 12 Diff: 2 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

39) a) By how much can the amount of space decrease before there is a change in the profit? b) By how much can the amount of space decrease before there is a change in the product mix? c) By how much can the amount of time available to set up the display can increase before the solution (product mix) would change? d) What is the lowest value for the amount of time available to set up the display increase before the solution (product mix) would change? Answer: a) 0 b) 8 c) 0 d) 57 Diff: 3 Page Ref: 88 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

40) You are offered the chance to obtain more space. The offer is for 15 units and the total price is $1500. What should you do? Why? Answer: Reject the offer. (11 × 15) = 1125 < 1500 Diff: 2 Page Ref: 88 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

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41) Max Z = 5x1 + 3x2 Subject to:

6x1 + 2x2 ≤ 18 15x1 + 20x2 ≤ 60 x1, x2 ≥ 0

Determine the sensitivity range for each constraint. Answer: constraint 1: 6 - 24 constraint 2: 45 - 180 Diff: 3 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, sensitivity range for right hand sides AACSB: Analytical thinking

42) Max Z = 5x1 + 3x2 Subject to: 6x1 + 2x2 ≤ 18 15x1 + 20x2 ≤ 60 x1, x2 ≥ 0 Determine the sensitivity range for each objective function coefficient. Answer: x1: 2.25 - 9.0, x2: 1.667 - 6.667 Diff: 3 Page Ref: 84 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis/range for objective function coefficients AACSB: Analytical thinking

43) Max Z = 3x1 + 3x2 Subject to: 10x1 + 4x2 ≤ 60 25x1 + 50x2 ≤ 200 x1, x2 ≥ 0 Determine the sensitivity range for each objective function coefficient. Answer: x1: 1.5 - 7.5, x2: 1.2 - 6.0 Diff: 3 Page Ref: 84 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis/range for objective function coefficients AACSB: Analytical thinking

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Ch03 - The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. 44) What are the appropriate objective function and constraints for this scenario? Answer: Max Z = 1500B + 5000C + 17000E subject to: 900B + 1500C + 5000E ≤ 150,000 E≥5 C ≥ 12 B≥7 B ≤ 28 C-B≤0 Diff: 3 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

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45) Captain Stubing runs the LP model associated with the scenario and reads the following about the variable cells in the Excel sensitivity report. Provide an interpretation. Final Reduced Objective Allowable Value Cost Coefficient Increase

Cell

Name

$B$2 $C$2 $D$2

Bar Food Excursion

12 12 24.24

0 0 0

1500 5000 17000

1560 1660 1E+30

Allowable Decrease 1E+30 1E+30 3458.33333

Answer: There should be 12 different bar setups and cuisine types and 24.24 excursions. The Bar decision variable has an allowable increase of $1,560, so if the profit on a bar setup increased by that amount over the current value, i.e., all the way up to $3,060, the bar setups would remain the same at 12. The food types can increase by up to $1,660 per type, or up to $6,660 while remaining at 12 as the best number. Excursion profit can drop by up to $3,458 from the current value of $17,000 without changing from the recommended 24.24 value. The actual profit earned would of course change if these parameters stayed within their allowable increases and decreases, but the number of food, bar, and excursion types would remain at 12, 12 and 24 (and some change). Diff: 3 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

46) Captain Stubing runs the LP model associated with the scenario and reads the following about the constraints in the Excel sensitivity report. Gopher is unable to provide an interpretation, but you volunteer to provide insight on the Restaurant and Excursions portion of the sensitivity report.

Cell

Name

$E$10 Bar/Food $E$11 Budget $E$6 Excursions $E$7 Restaurant

Final Value 0 150000 24.24 12

Shadow Constraint Allowable Price R.H. Side Increase 1560 3.4 0 -1660

0 150000 5 12

5 1E+30 19.24 16

Allowable Decrease 16 96200 1E+30 5

Answer: The Restaurant constraint has a shadow price of -$1,660 which means that for every one more cuisine variety required, the profit will drop by $1,660. If we required two more, profit would drop by $3320, and so on, up to requiring 16 additional meal types. Beyond that, the $1,660 cost would not be a correct estimate. For each type of cuisine dropped, from 12 to 11, the same figure hold, up to a reduction of five types of cuisine. Excursions has no shadow price – it is not a binding constraint, so we can actually reduce the number of excursions quite a bit, but 19.24 down to the required minimum of 5 per day. Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

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47) Using just the Constraints portion of the sensitivity report, indicate which of Captain Stubing's limitations are reducing his profit.

Cell

Name

$E$10 Bar/Food $E$11 Budget $E$6 Excursions $E$7 Restaurant $E$8 Bar Low $E$9 Bar High

Final Value 0 150000 24.24 12 12 12

Shadow Constraint Allowable Price R.H. Side Increase 1560 3.4 0 -1660 0 0

0 150000 5 12 7 28

5 1E+30 19.24 16 5 1E+30

Allowable Decrease 16 96200 1E+30 5 1E+30 16

Answer: Three of the constraints have shadow prices of zero, meaning they are non-binding and thus do not limit his profit. The Bar/Food combination, that is the requirement that there should be at least one bar type for each cuisine type, is holding him back. The budget constraint also limits the profit, for each additional budget dollar he had to start the cruise, he could generate an additional $3.40. If the right hand side of these constraints were increased, then additional profit could be earned. The restaurant constraint also limits profit, but since the shadow price is negative, an additional increase of the RHS reduces the profit. If the number of cuisine type drops by one, the an additional $1,660 can be made. Diff: 3 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

48) Captain Stubing eyes the sensitivity report for his decision variables and Julie McCoy, Cruise Director, studies it. Her sneeze obscures part of the printout, leaving the captain scratching his head about the values of each of the three variables, Bar, Food and Excursion. Does he need all three? How would he know simply by reading the remaining legible portion of the report?

Cell

Name

$B$2 Bar $C$2 Food $D$2 Excursion

Final Reduced Objective Allowable Value Cost Coefficient Increase 12 12 24.24

0 0 0

1500 5000 17000

1560 1660 1E+30

Allowable Decrease 1E+30 1E+30 3458.33333

Answer: As luck would have it, we know that all three have positive values in the final solution. None of them shows as having a reduced cost, which means that they all must be in the solution. Diff: 2 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

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49) Provide an interpretation of the Ranging Report from QM

Answer: There should be 12 different bar setups and cuisine types and 24.24 excursions. The Bar decision variable has an upper bound of $3,060, so if the bar profit increases all the way up to $3,060, the bar setups would remain the same at 12. The food types can increase by up to $1,660 per type, or up to $6,660 while remaining at 12 as the best number. Excursion profit can drop by up to $3,458 from the current value of $17,000 without changing from the recommended 24.24 value. The actual profit earned would of course change if these parameters stayed within their allowable increases and decreases, but the number of food, bar, and excursion types would remain at 12, 12 and 24 (and some change). Diff: 3 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

50) Provide an interpretation of the Budget, Excursions constraints portion of the Ranging report for Captain Stubing.

Answer: The Restaurant constraint has a dual value of -$1,660 which means that for every one more cuisine variety required, the profit will drop by $1,660. If we required two more, profit would drop by $3,320, and so on, up to requiring 16 additional meal types. Beyond that, the $1,660 cost would not be a correct estimate. For each type of cuisine dropped, from 12 to 11, the same figure hold, up to a reduction of five types of cuisine. Excursions has no dual value - it is not a binding constraint, so we can actually reduce the number of excursions quite a bit, but 19.24 down to the required minimum of 5 per day. Diff: 3 Page Ref: 83 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

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51) Interpret this sensitivity report for the variable cells.

Cell

Final Reduced Objective Name Value Cost Coefficient

$B$13 A $C$13 B $D$13 C

9 0 0

0 -2 -2

Allowable Increase

5 6 1

1E+30 2 2

Allowable Decrease 1.25 1E+30 1E+30

Answer: Decision variable A is the only variable that appears in the optimal answer. Nine units of A are optimal and the coefficient is 5, so the objective function value is 45. The optimal answer will remain nine units of A as long as the coefficient remains in the range of 3.75 to infinity. Decision variable B, with a coefficient of 6, is not used in the optimal answer. If the coefficient of B increased to 8 or beyond, it would enter the model with a positive value. If the value of B's coefficient drops by any amount, it will not enter the decision space. Similarly, C with an objective coefficient of 1, is not in the answer unless the coefficient increases to 3 or beyond. If we added a constraint that required either B or C to enter the solution, the value of the objective function would drop by 2, from 45 to 43. Diff: 3 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficients AACSB: Analytical thinking

52) Interpret this sensitivity report for the constraints.

Cell

Final Shadow Constraint Name Value Price R.H. Side

$E$15 One $E$16 Two $E$17 Three $E$18 Four

45 54 27 72

1 0 0 0

45 56 67 78

Allowable Increase 1.666666667 1E+30 1E+30 1E+30

Allowable Decrease 45 2 40 6

Answer: Constraint One is the only binding constraint; it has a shadow price of 1, meaning that if the RHS increased by 1, the optimal value of the objectgive function would rise by 1. This works in the very limited range up to 46.6666667. If the RHS dropped by 1, the objective function value would drop by 1 all the way down to a RHS equal to 0. The other constraints have slack; if constraint Two's RHS drops by 2 or more, the optimal answer would change. Constraint Four would become binding if the RHS was 72 or lower and constraint Three enters the picture if the RHS drops to 27 or lower. For the moment, any increase in the RHS for Two, Three or Four would have no impact on the optimal answer. Diff: 3 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking

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53) For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs. and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: A) same product mix, different total profit. B) different product mix, same total profit as before. C) same product mix, same total profit. D) different product mix, different total profit. Answer: A Diff: 2 Page Ref: 89 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

54) A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 300 minutes, providing two additional machine hours will result in: A) the same product mix, different total profit. B) a different product mix, same total profit as before. C) the same product mix, same total profit. D) a different product mix, different total profit. Answer: D Diff: 3 Page Ref: 88 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. 55) If the production manager decides to produce of 400 bottles of light beer and 0 bottles of dark beer, it will result in slack of: A) malt only. B) wheat only. C) both malt and wheat. D) neither malt nor wheat. Answer: B Diff: 2 Page Ref: 84 Section Heading: Sensitivity Analysis and Graphical Solution Keywords: graphical solution, constraints AACSB: Analytical thinking

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56) Which of the following is not a feasible solution? A) 0 L and 0 D B) 0 L and 400 D C) 200 L and 300 D D) 300 L and 200 D Answer: D Diff: 3 Page Ref: 84 Section Heading: Sensitivity Analysis Keywords: computer solution, infeasibility AACSB: Analytical thinking

57) What is the optimal weekly profit? A) $1000 B) $900 C) $800 D) $700 Answer: C Diff: 2 Page Ref: 78 Section Heading: Computer Solution Keywords: computer solution AACSB: Analytical thinking

58) Which of the following could not be a linear programming problem constraint? A) A + B ≤ -3 B) A - B ≤ -3 C) A - B ≤ 3 D) -A + B ≤ -3 Answer: A Diff: 2 Page Ref: 78 Section Heading: Computer Solution Keywords: graphical solution, feasibility AACSB: Analytical thinking

59) Use the constraints given below and determine which of the following points is feasible. (1) 14x + 6y ≤ 42 (2) x - y ≤ 3 A) x = 1; y = 4 B) x = 2; y = 8 C) x = 2; y = 4 D) x = 3; y = 0.5 Answer: A Diff: 2 Page Ref: 84 Section Heading: Sensitivity Analysis Keywords: constraints AACSB: Analytical thinking

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60) For the constraints given below, which point is in the feasible region of this minimization problem? (1) 14x + 6y ≤ 42 (2) x + 3y ≥ 6 A) x = 2; y = 5 B) x = 1; y = 2 C) x = 2; y = 1 D) x = 2; y = 3 Answer: B Diff: 2 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: constraints AACSB: Analytical thinking

61) What combination of x and y is a feasible solution that minimizes the value of the objective function? Min Z = 3x + 15y (1) 2x + 4y ≥ 12 (2) 5x + 2y ≥10 A) x = 0; y = 3 B) x = 0; y = 5 C) x = 5; y = 0 D) x = 6; y = 0 Answer: C Diff: 3 Page Ref: 80 Section Heading: Computer Solution Keywords: feasibility, constraints AACSB: Analytical thinking

62) A shadow price reflects which of the following in a maximization problem? A) the marginal gain in the objective that would be realized by adding one unit of a resource B) the marginal gain in the objective that would be realized by subtracting one unit of a resource C) the marginal cost of adding additional resources D) the marginal gain of selling one more unit Answer: A Diff: 3 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: shadow price, sensitivity analysis AACSB: Analytical thinking

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63) Given the following linear programming problem: Max Z = 15x + 20y s.t. 8x + 5y ≤ 40 4x + y ≥ 4 What would be the values of x and y that will maximize revenue? A) x = 5; y = 0 B) x = 0; y = 8 C) x = 0; y = 1 D) x = 1; y = 0 Answer: B Diff: 2 Page Ref: 780 Section Heading: Computer Solution Keywords: formulation, solution AACSB: Analytical thinking

64) Given the following linear program that maximizes revenue: Max Z = 15x + 20y s.t. 8x + 5y ≤ 40 4x + y ≥ 4 What is the maximum revenue at the optimal solution? A) $120 B) $160 C) $185 D) $200 Answer: B Diff: 2 Page Ref: 74 Section Heading: Computer Solution of a Transportation Problem Keywords: formulation, solution AACSB: Analytical thinking

65) For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________. A) decrease, resource B) increase, parameter C) improvement, resource D) decrease, parameter Answer: C Diff: 2 Page Ref: 90 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

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66) Sensitivity analysis is the analysis of the effect of ________ changes on the ________. A) price, company B) cost, production C) parameter, optimal solution D) constraint, parameter Answer: C Diff: 1 Page Ref: 82 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking

67) For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint: A) will have a positive value. B) will have a negative value. C) will have a value of zero. D) could have a positive, negative or a value of zero. (no sign restrictions). Answer: C Diff: 3 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking

68) For a resource constraint, either its slack value must be ________ or its shadow price must be ________. A) negative, negative B) negative, zero C) zero, zero D) zero, negative Answer: C Diff: 1 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking

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Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table:

Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report:

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The Sensitivity Report:

69) Which additional resources would you recommend that Aunt Anastasia try to obtain? A) mix/mold B) kiln C) paint and seal D) demand Answer: B Diff: 1 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

70) Suppose the charitable organization contacted Aunt Anastasia and told her that they had underestimated the amount of rabbits they needed. Instead of 25 rabbits, they need 35. How would this affect Aunt Anastasia's profits? A) Profits would increase by $5. B) Profits would decrease by $5. C) Profits would increase by $2.50. D) Profits would decrease by $2.50. Answer: B Diff: 3 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

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71) Aunt Anastasia feels that her prices are too low, particularly for her eggs. How much would her profit have to increase on the eggs before it is profitable for her to make and sell eggs? A) $0.50 B) $1.00 C) $1.50 D) $2.50 Answer: B Diff: 2 Page Ref: 90 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

72) Aunt Anastasia's available hours for paint and seal have fallen from 80 hours to 60 hours because of other commitments. How will this affect her profits? A) Profits will increase by $30. B) Profits will decrease by $20. C) Profits will increase by $20. D) Profits will not change. Answer: D Diff: 2 Page Ref: 90 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

73) Aunt Anastasia can obtain an additional 10 hours of kiln capacity free of charge from a friend. If she did this, how would her profits be affected? A) Profit would increase by $25. B) Profits would decrease by $25. C) Profits would decrease by $6.25. D) Cannot tell from the information provided. Answer: D Diff: 2 Page Ref: 90 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

74) Aunt Anastasia is planning for next spring, and she is considering making only two products. Based on the results from the linear program, which two products would you recommend that she make? A) baskets and eggs B) baskets and rabbits C) eggs and rabbits D) She should continue to make all three. Answer: B Diff: 2 Page Ref: 80 Section Heading: Computer Solution Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking

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Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time and 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time and 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3750 labor hours, and he has a budget of $3000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25. The LP formulation that maximizes week profit shown below. MAX 15A +18B + 25 C s.t. 2A + 2.5B + 3C ≤ 300 20A + 30B + 45C ≤ 3750 10A + 14B + 18C ≤ 3000 The solution from QM for Windows is show below.

75) If Billy could acquire more of any resource, which would it be? A) machining time B) labor time C) money D) buyers Answer: A Diff: 2 Page Ref: 85 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking

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76) If one of Billy's machines breaks down, it usually results in about 6 hours of downtime. When this happens, Billy's profits are reduced by: A) $15. B) $18. C) $25. D) $35. Answer: D Diff: 2 Page Ref: 84 Section Heading: Linear Programming Models Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking

77) Billy's accountant made an error, and the budget has been reduced from $3000 to $2500. Billy's profit will go down by: A) $0. B) $625. C) $1350. D) $1650. Answer: A Diff: 2 Page Ref: 86 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking

78) Billy has decided that he can raise the price on the Curious t-shirt by 10% without losing sales. If he raises the price, his profits will: A) increase by 10%. B) decrease by 10%. C) increase by $2.50. D) increase by $125. Answer: D Diff: 2 Page Ref: 85 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking

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79) The local cheese vendor offers to sell Taco Loco 200 pounds of cheese for these three products. Taco Loco should: A) refuse to buy any cheese. B) buy less than 80 pounds of cheese for $1.45 per pound. C) buy 46 pounds or less of cheese for $1.45 or less. D) buy at least 126 pounds of cheese for $5.33 or less. Answer: C Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: shadow price, computer solution AACSB: Analytical thinking

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80) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. Answer: C Diff: 2 Page Ref: 80 Section Heading: Computer Solution Keywords: computer solution, spreadsheets AACSB: Analytical thinking

81) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds Answer: C Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking

82) How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z? A) 28.73 B) 39.27 C) 0 D) 1E+30 Answer: A Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking

83) What is the increase in revenue if Taco Loco purchases 20 pounds of cheese for $1 and uses it optimally? A) $0 B) $9.09 C) $29.00 D) $158.18 Answer: C Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: shadow price, sensitivity analysis AACSB: Analytical thinking

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Ch03 - The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. 84) What should Captain Stubing's objective function be? A) Max Z = 1500 Bar + 5000 Food + 17000 Excursion B) Max Z = Bar + Food + Excursion C) Max Z = 900 Bar + 1500 Food + 5000 Excursion D) Max Z = 5 Excursions + 12 Cuisine + 7 Bar + 150000 Budget Answer: A Diff: 2 Page Ref: 77 Section Heading: Sensitivity Analysis Keywords: objective function AACSB: Analytical thinking

85) What is the appropriate constraint for the budget? A) 1 Bar + 1 Food + 1 Excursion ≤ 150,000 B) 900 Bar + 1500 Food + 5,000 Excursion ≤ 150,000 C) 1,500 Bar + 5,000 Food + 17,000 Excursion ≤ 150,000 D) 7 Bar + 12 Food + 5 Excursion ≤ 150,000 Answer: B Diff: 2 Page Ref: 78 Section Heading: Sensitivity Analysis Keywords: constraints AACSB: Analytical thinking

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86) What is the appropriate constraint for the requirement that there should be at least one different bar setup for every different type of food? A) Bar - Food ≤ 0 B) Bar + Food ≤ 0 C) Food - Bar ≤ 0 D) Food + Bar ≥ 0 Answer: C Diff: 2 Page Ref: 78 Section Heading: Sensitivity Analysis Keywords: constraints, formulation AACSB: Analytical thinking

87) Here's the sensitivity report for the decision variables. Which of these conclusions is correct?

Cell

Name

$B$2 Bar $C$2 Cuisine $D$2 Excursion

Final Reduced Objective Allowable Value Cost Coefficient Increase 12 12 24.24

0 0 0

1500 5000 17000

1560 1660 1E+30

Allowable Decrease 1E+30 1E+30 3458.333333

A) If the cost of the Bar variable is reduced by more than 0, then more of it will be used. B) If the cost of the Bar variable is increased by more than 0, then more of it will be used. C) If the coefficient for the Cuisine variable rises to 1660, then more of it will be used. D) It doesn't matter how much money they make on excursions, the optimal answer will continue to be 24.24 of them. Answer: D Diff: 2 Page Ref: 90 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficients AACSB: Analytical thinking

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88) Here's a portion of the sensitivity analysis for the constraints. Which of these statements is best?

Cell

Name

$E$10 Bar/Food $E$11 Budget $E$6 Excursions $E$7 Restaurant

Final Value 0 150000 24.24 12

Shadow Constraint Allowable Price R.H. Side Increase 1560 3.4 0 -1660

0 150000 5 12

Allowable Decrease

5 1E+30 19.24 16

16 96200 1E+30 5

A) If the budget rises to $150,001, then the optimal mix will result in an increased revenue of $3.40. B) If the excursions rise to 6, then the optimal mix will result in increased revenue of $19.24. C) If the restaurant constraint increased to 13, the optimal mix will result in increased revenues of $1,660. D) If the bar/food constraint rises to 1560, then the revenue will rise by a factor of 16. Answer: A Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking

89) Based on the variable cells sensitivity report, what conclusion is best?

Cell

Name

$B$2 Bar $C$2 Cuisine $D$2 Excursion

Final Reduced Objective Allowable Value Cost Coefficient Increase

Allowable Decrease

12 12 24.24

1E+30 1E+30 3458.333333

0 0 0

1500 5000 17000

1560 1660 1E+30

A) The value of Excursion can be infinite, since 1E+30 is 10 to the 30th power. B) The values of Bar, Cuisine, and Excursion are all equal to zero. C) The values of Bar and Cuisine can be negative since they have allowable decreases of 1E+30. D) The optimal value for the objective function is $490,080 Answer: D Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: objective function AACSB: Analytical thinking

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90) Here's a lovely portion of the sensitivity report for the constraints. Which of these conclusions is reasonable? Cell

Name

$E$10 Bar/Food $E$11 Budget $E$6 Excursions $E$7 Restaurant $E$8 Bar Low $E$9 Bar High

Final Value 0 150000 24.24 12 12 12

Shadow Constraint Price R.H. Side 1560 3.4 0 -1660 0 0

0 150000 5 12 7 28

A) Captain Stubing is scheduling more Excursions than he should be. B) Captain Stubing should exhaust his Budget. C) There is no Bar or Food being used. D) The value for Restaurant will rise by $1,660 for each additional cuisine required. Answer: B Diff: 2 Page Ref: 92 Section Heading: Sensitivity Analysis Keywords: objective function AACSB: Analytical thinking

91) How should the requirement that the bar setups should change at least every other day but no more than twice per day? A) 1 Bar ≥ 7 1 Bar ≤ 28 B) 7 ≤ 1 Bar ≤ 28 C) 1 Bar ≤ 28 D) 1 Bar ≥ 7 Answer: A Diff: 2 Page Ref: 82 Section Heading: Sensitivity Analysis Keywords: objective function AACSB: Analytical thinking

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92) Using this snippet of the sensitivity report for variable cells, which of these conclusions is best?

Cell

Final Reduced Objective Name Value Cost Coefficient

$B$13 A $C$13 B $D$13 C

9 0 0

0 -2 -2

Allowable Increase

5 6 1

1E+30 2 2

Allowable Decrease 1.25 1E+30 1E+30

A) Item A can drop in value all the way down to 1.25 before it harms the result. B) Items B and C are the only elements in the final model. C) The final value of this problem is 9. D) Insisting that one additional unit of B, be included in the model will reduce the profit by $2. Answer: D Diff: 1 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficients AACSB: Analytical thinking

93) Using this snippet of the sensitivity report for constraints, which of these conclusions is best?

Cell

Final Shadow Constraint Name Value Price R.H. Side

$E$15 One $E$16 Two $E$17 Three $E$18 Four

45 54 27 72

1 0 0 0

45 56 67 78

Allowable Increase 1.666666667 1E+30 1E+30 1E+30

Allowable Decrease 45 2 40 6

A) None of items Two, Three or Four is being used. B) Adding two units of One will increase the objective function value by two. C) Taking away four units of One will lower the objective function value by four. D) The most valuable resource is Four. Answer: C Diff: 2 Page Ref: 87 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 4 Linear Programming: Modeling Examples 1) Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem. Answer: TRUE Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: formulation, product mix problem AACSB: Analytical thinking

2) Product mix problems cannot have greater-than-or-equal-to (≥) constraints. Answer: FALSE Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking

3) When using a linear programming model to solve the diet problem, the objective is generally to maximize profit. Answer: FALSE Diff: 2 Page Ref: 119-122 Section Heading: A Diet Example Keywords: objective function AACSB: Analytical thinking

4) When using a linear programming model to solve the diet problem, the objective is generally to maximize nutritional content. Answer: FALSE Diff: 2 Page Ref: 119-122 Section Heading: A Diet Example Keywords: objective function AACSB: Analytical thinking

5) Diet problems usually maximize nutritional value. Answer: FALSE Diff: 2 Page Ref: 119-122 Section Heading: A Diet Example Keywords: diet example AACSB: Application of knowledge

6) In most media selection decisions, the objective of the decision maker is to minimize cost. Answer: FALSE Diff: 2 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Application of knowledge

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7) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure. Answer: TRUE Diff: 2 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Application of knowledge

8) A linear programming model of a media selection problem is used to determine the relative value of each advertising media. Answer: FALSE Diff: 3 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Application of knowledge

9) In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. Answer: TRUE Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Analytical thinking

10) The constraint x + y = z is written in standard form. Answer: FALSE Diff: 2 Page Ref: 123 Section Heading: An Investment Example Keywords: standard form AACSB: Application of knowledge

11) In an unbalanced transportation model, supply does not equal demand, and supply constraints have ≤ signs. Answer: TRUE Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Analytical thinking

12) Transportation problems can have solution values that are non-integer and must be rounded. Answer: FALSE Diff: 3 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation problem, solution AACSB: Analytical thinking

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13) In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill). Answer: TRUE Diff: 1 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Application of knowledge

14) In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store). Answer: TRUE Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Application of knowledge

15) A conservative approach to a balanced transportation model would be to make all constraints lessthan-or-equal-to constraints. Answer: FALSE Diff: 2 Page Ref: 133 Section Heading: A Transportation Example Keywords: balanced transportation model, transportation model formulation AACSB: Application of knowledge

16) In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). Answer: FALSE Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Application of knowledge

17) Blending problems usually require algebraic manipulation in order to write the LP in "standard form." Answer: TRUE Diff: 1 Page Ref: 135-138 Section Heading: A Blend Example Keywords: blending AACSB: Application of knowledge

18) Fractional relationships among variables are considered standard form in a blending problem. Answer: FALSE Diff: 1 Page Ref: 136 Section Heading: A Blend Example Keywords: blending AACSB: Application of knowledge

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19) Data envelopment analysis indicates which type of service unit makes the highest profit. Answer: FALSE Diff: 1 Page Ref: 144-148 Section Heading: A Data Envelopment Analysis Example Keywords: blending AACSB: Analytical thinking

20) In a classic blending problem, revenue is maximized by subtracting cost from profit. Answer: FALSE Diff: 1 Page Ref: 135 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking

21) Data envelopment analysis problems are usually maximization problems. Answer: TRUE Diff: 1 Page Ref: 145 Section Heading: A Data Envelopment Analysis Example Keywords: data envelopment analysis AACSB: Application of knowledge

22) Data envelopment analysis indicates the relative ________ of a service unit compared with others. Answer: efficiency or productivity Diff: 2 Page Ref: 144-148 Section Heading: A Data Envelopment Analysis Example Keywords: data envelopment analysis AACSB: Application of knowledge

23) ________ types of linear programming problems often result in fractional relations between variables which must be eliminated. Answer: Blending Diff: 2 Page Ref: 135-138 Section Heading: A Blend Example Keywords: blending AACSB: Application of knowledge

24) Cranky Jerry's Furniture Factory makes tables and chairs. If he is interested in a profit maximizing level of production, he should probably follow the example for the ________ problem found in this chapter. Answer: product mix Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: product mix AACSB: Application of knowledge

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25) When the ________ command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed. Answer: SUMPRODUCT Diff: 2 Page Ref: 119-122 Section Heading: A Diet Example Keywords: spreadsheet solution AACSB: Application of knowledge

26) Cranky Jerry's Day Care wants to minimize their food cost while meeting the minimum (and I mean bare minimum) guidelines for nutrition as set forth by the state. The best approach would be to follow the example in this chapter for a(n) ________ problem. Answer: diet Diff: 2 Page Ref: 119-122 Section Heading: A Diet Example Keywords: diet example AACSB: Application of knowledge

27) The ________ for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign. Answer: standard form Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: formulation, constraints AACSB: Application of knowledge

28) The objective function of a diet problem is usually to ________ subject to nutritional requirements. Answer: minimize costs Diff: 1 Page Ref: 119-122 Section Heading: A Diet Example Keywords: diet problem AACSB: Analytical thinking

29) Investment problems maximize ________. Answer: return on investments Diff: 1 Page Ref: 122-127 Section Heading: An Investment Example Keywords: investment AACSB: Application of knowledge

30) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the ________. Answer: audience exposure Diff: 2 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Analytical thinking

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31) In a(n) ________ problem, maximization of audience exposure may not result in maximization of total profit. Answer: media selection Diff: 3 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Application of knowledge

32) In a balanced transportation model, supply equals ________. Answer: demand Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Application of knowledge

33) A balanced transportation model should have ________ constraints. Answer: = or "equal to" Diff: 2 Page Ref: 133 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Analytical thinking

34) There are three plants scattered across the United States that manufacture Dull computers. These plants assemble products for customers throughout the United States, Canada, and Mexico. If Dull wishes to maximize profit by choosing the most economical pair of factory and customer for each order, they would be well-advised to follow the ________ model presented in this chapter. Answer: transportation problem Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation model AACSB: Application of knowledge

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50. 35) What is the formulation for this problem? Answer: MAX Z = 0. 4L + 0.5V s.t. 2L + 3V ≤ 4800 6L + 8V ≤ 9600 1L + 2V ≤ 2000 Diff: 1 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: computer solution AACSB: Analytical thinking

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36) For the production combination of 800 bags of lime and 600 bags of vinegar, which resource is not completely used up and how much is remaining? Answer: salt only, 1400 ounces remaining Diff: 1 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: slack, computer solution AACSB: Analytical thinking

37) The production combination of 450 bags of lime and 800 bags of vinegar is not feasible because one resource is exceeded. Which resource is exceeded and how much more is needed to produce this combination? Answer: herbs only, 50 ounces are needed Diff: 1 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: slack, computer solution AACSB: Analytical thinking

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. The shop must produce at least 400 almond-filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. 38) This represents what type of linear programming application? Answer: product mix Diff: 1 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: computer solution AACSB: Application of knowledge

39) What is the formulation for this problem? Answer: MAX Z = $.20B + $.30C s.t. 6B + 3C ≤ 6600 1B + 1C ≤ 1400 2B + 4C ≤ 4800 C ≥ 400 Diff: 1 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: formulation, constraints AACSB: Analytical thinking

40) For the production combination of 600 bear claws and 800 almond-filled croissants, how much flour and almond paste are remaining? Answer: flour = 600 ounces, almond paste = 400 TS Diff: 1 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: slack, computer solution AACSB: Analytical thinking

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41) If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company's three products in period 2 is 400. Answer: X12 + X22 + X32 ≤ 400 Diff: 2 Page Ref: 139-144 Section Heading: A Multiperiod Scheduling Example Keywords: transportation problem, supply constraint AACSB: Analytical thinking

Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Newspaper Radio Twitter Facebook

Exposure 5,000 3,000 700 200

Cost $500 $250 $25 $15

The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) 42) Formulate the appropriate objective function for this scenario. Answer: Max Z = 5,000x1 + 3,000x2 + 700x3 + 200x4 Where x1 = Newspaper advertisements x2 = Radio advertisements x3 = Tweets x4 = Facebook postings Diff: 2 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: linear programming formulation AACSB: Analytical thinking

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43) Formulate the appropriate LP model for this scenario. Answer: Max Z = 5,000x1 + 3,000x2 + 700x3 + 200x4 Where x1 = Newspaper advertisements x2 = Radio advertisements x3 = Tweets x4 = Facebook postings Subject to: $500x1 + $250x2 + $125x3 + $15x4 ≤ $3,500 x1 ≤ 4 x2 ≤ 24 x3 ≤ 3 x4 ≤ 4 Diff: 2 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: linear programming formulation AACSB: Analytical thinking

44) The Excel LP model for this scenario shows the following sensitivity report for the variable cells . Comment on the salient features.

Cell

Name

$C$2 Newspaper $D$2 Radio $E$2 Twitter $F$2 Facebook

Final Reduced Objective Value Cost Coefficient 0 13.76 0 4

-1000 0 -800 0

Allowable Increase

5000 3000 700 200

1000 333.3333333 800 1E+30

Allowable Decrease 1E+30 500 1E+30 2

Answer: The model recommends four Facebook postings and almost 14 radio spots which will reach 42,080 potential tourists. Forcing the two unchosen media would result in a drop of 1000 customers if newspaper entered the marketing mix and a drop of 800 customers if Twitter was required. The Facebook allowable decrease is of some concern among all shown as the decrease of 2 units is small by comparison to the other ranges shown for the newspaper, radio and Twitter channels. Diff: 2 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: linear programming formulation AACSB: Analytical thinking

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45) The Excel LP model for this scenario shows the following sensitivity report for the constraints. Comment on the salient features. Cell

Name

$G$5 Budget $G$6 Newspaper $G$7 Radio $G$8 Twitter $G$9 Facebook

Final Shadow Constraint Value Price R.H. Side 3500 0 13.76 0 4

12 0 0 0 20

Allowable Increase

3500 4 24 3 4

2560 1E+30 1E+30 1E+30 229.3333333

Allowable Decrease 3440 4 10.24 3 4

Answer: The budget has a shadow price of 12, meaning that for every $1 increase in budget, an additional 12 customers could be reached. Facebook's shadow price of 20 can be interpreted as an increase in 20 customers receiving the message for each additional Facebook posting up to 233 postings. Newspaper and Twitter are not in the model and thus have no opportunity cost in this formulation. The budget shadow price is robust, but that of Facebook is comparatively narrow. Diff: 2 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: linear programming formulation AACSB: Analytical thinking

46) Small motors for garden equipment are produced at four manufacturing facilities and need to be shipped to three plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the three different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility.

Write the formulation for this problem. Answer: MIN Z = 4x1A + 4.5x1B + 3.2x1C + 3.5x2A + 3x2B + 4x2C + 4x3A + 3.5x3B + 4.25x3C s.t. x1A + x1B +x1C = 200 x2A + x2B +x2C = 200 x3A + x3B +x3C = 300 x1A + x2A +x3A = 250 x1B + x2B +x3B = 150 x1C + x2C +x3C = 200 Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: computer solution, transportation/distribution AACSB: Analytical thinking

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47) Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How much oil-based and water-based paint should the Quickbrush make? Answer: 9167 gallons of water-base paint and 5833 gallons of oil-base paint Diff: 2 Page Ref: 135-138 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking

Andy Tyre manages Tyre's Wheels, Inc. Andy has received an order for 1000 standard wheels and 1200 deluxe wheels for next month, and for 750 standard wheels and 1000 deluxe wheels the following months. He must fill all the orders. The cost of regular time production for standard wheels is $25 and for deluxe wheels, $40. Overtime production costs 50% more. For each of the next two months there are 1000 hours of regular time production and 500 hours of overtime production available. A standard wheel requires .5 hour of production time and a deluxe wheel, .6 hour. The cost of carrying a wheel from one month to the next is $2. 48) Define the decision variables and objective function for this problem. Answer: Define the decision variables: S1R = number of standard wheels produced in month 1 on regular time production S1O = number of standard wheels produced in month 1 on overtime production S2R = number of standard wheels produced in month 2 on regular time production S2O = number of standard wheels produced in month 2 on overtime production D1R = number of deluxe wheels produced in month 1 on regular time production D1O = number of deluxe wheels produced in month 1 on overtime production D2R = number of deluxe wheels produced in month 2 on regular time production D2O = number of deluxe wheels produced in month 2 on overtime production Y1 = number of standard wheels stored from month 1 to month 2. Y2 = number of deluxe wheels stored from month 1 to month 2. MIN 25 S1R + 37.5 S1O + 40 D1R + 60 D1O + 25 S2R + 37.5 S2O + 40 D2R + 60 D2O + 2 Y1 + 2 Y2 Diff: 2 Page Ref: 139-144 Section Heading: A Multiperiod Scheduling Example Keywords: linear programming multiperiod scheduling AACSB: Analytical thinking

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49) Write the constraints for this problem. Answer: S1R + S1O - Y1 = 1000 .5 S1R + .6 D1R ≤ 1000 D1R + D1O - Y2 = 1200 S2R + S2O + Y1 = 750

.5 S1O + .6 D1O ≤ 500

D2R + D2O + Y2 = 1000

.5 S2R + .6 D2R ≤ 1000 .5 S2O + .6 D12O ≤ 500

Diff: 2 Page Ref: 139-144 Section Heading: A Multiperiod Scheduling Example Keywords: linear programming multiperiod scheduling AACSB: Analytical thinking

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week. The table below shows relevant manufacturing information:

Shirt

Total Yards of Fabric per Shirt

Athletic

1.00

Varsity

1.20

Surfer

0.90

Fabric Requirement at least 60% cotton no more than 30% rayon as much as 80% cotton

Minimum Weekly Contracts

Maximum Demand

Selling Price

500

600

$30

650

850

$40

300

700

$36

50) Assume that the decision variables are defined as follows: A = total number of athletic shirts produced V = total number of varsity shirts produced S = total number of surfer shirts produced C = yards of cotton purchased R = yards of rayon purchased Xij = yards of fabric i (C or R) blended into shirt j (A, V or S) Write the objective function. Answer: max 30 A + 40 V + 36 S - 5C - 7R Diff: 2 Page Ref: 135-138 Section Heading: A Blend Example Keywords: objective function, model construction AACSB: Analytical thinking

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51) Write the constraints for the fabric requirements. Answer: Form of constraints: Total yards used is greater than (or less than) total yards required × (% fabric required) shirts produced. XCA ≥ 0.6 A XVR ≤ 0.36V XSC ≤ 0.72 S Diff: 2 Page Ref: 135-138 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking

52) Write the constraints for the total number of shirts of each style produced. Answer: Form of constraint: number of shirts produced = (total yards used to make the shirt)/(yards/shirt) A = (XCA + XRA)/1 V = (XCV + XRV)/1.2 S = (XCS + XRS)/0.9 Standard form: A - XCA - XRA = 0 1.2 V - XCV - XRV = 0 0.9 S - XCS - XRS = 0 Diff: 3 Page Ref: 135-138 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking

53) Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows:

Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan, and how much fat and protein do the cats receive? Answer: Cost is $3.60, which uses 14 ounces of Meow Munch and 5.33 ounces of Feline Feed. Diff: 2 Page Ref: 119-122 Section Heading: A Diet Example Keywords: diet AACSB: Analytical thinking

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Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Eggs/week Plumage Temperament Fertilizer Appetite

Leghorn 5 3 2 3 5

Cochin 2 9 8 2 4

Buff Orpington 4.5 6 5 4 8

Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. 54) How should the objective function read? Answer: Max Z = 5L + 2C + 4.5B Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking

55) What is a full set of constraints if the farmer wants this flock to produce less than 100 decibels of noise and more than 5 pounds of fertilizer, consume less than 10 pounds of layer pellets, and achieve a total plumage score of at least 75? Answer: 3L + 9C+ 6B >= 75 2L + 8C + 5B <= 100 3L + 2C + 4B >= 80 5L + 4C + 8B <= 160 Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: constraints, formulation AACSB: Analytical thinking

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56) Formulate the objective function and constraints for this scenario. Answer: Max Z = 5L + 2C + 4.5B 3L + 9C+ 6B >= 75 Subject to: 2L + 8C + 5B <= 100 3L + 2C + 4B >= 80 5L + 4C + 8B <= 160 Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: formulation AACSB: Analytical thinking

57) The poultry farmer discovers, much to his dismay, that the product mix that satisfies all of his constraints isn't really a mix of birds—it's a flock consisting of nothing but 32 Leghorns. (His constraints were a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week.) Not only is his flock going to be a very one-note mix in terms of color, he is afraid that the gleaming white feathers and deafening noise will attract predators, or worse yet, his neighbors. He immediately embarks on a breeding program to develop a Super-Cochin that can lay 4.5 eggs per week with all other performance measures the same. His optimal solution is now 27.5 Leghorns and 5.625 Super-Cochins. Assuming that he is willing to settle for a flock that has 27 Leghorns and 5 Super Cochins, what is the weekly output of eggs and performance with respect to the constraints? Answer: He should get (27 × 5) + (4.5 × 5) = 157.5 eggs per week The plumage score is now 126. The fertilizer output is 91 ounces per week, The temperament score is 94. The appetite is 155 ounces of layer pellets per week. Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking

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58) A credit union wants to make investments in the following:

The firm will have $2,500,000 available for investment during the coming year. The following restrictions apply: • Risk-free securities may not exceed 30% of the total funds, but must comprise at least 5% of the total. • Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans). • Consumer loans plus other secured loans may not exceed the vehicle loans. • Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $2,500,000 be allocated to each alternative to maximize annual return? What is the annual return? Answer:

Diff: 3 Page Ref: 122-127 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking

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Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. 59) What is an appropriate objective function and constraints for this scenario? Answer: Max Z = 2.75N + 4B + 2Q + 3E subject to: Cheese 2N + 4B + 4Q + 3E ≤ 400 Meat 0N + 1B + 2Q + 2E ≤ 150 Beans 4N + 0B + 0Q + 2E ≤ 400 Tortilla 3N + 4B + 1Q + 3E ≤ 250 Diff: 3 Page Ref: 116 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking

60) What is an appropriate objective function for this scenario? Answer: Max Z = 2.75N + 4B + 2Q + 3E Diff: 2 Page Ref: 116 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking

61) The assistant manager had taken a management science class a few years before and while she knew enough to formulate the problem and implement it in Excel, the only sensitivity training she had ever received had to do with being more empathetic to the plight of her minimum wage workforce. Help her interpret the sensitivity report for the Nacholupa product as it appears below.

Cell

Name

$C$4

Nacholupa

Final Reduced Objective Value Cost Coefficient 55

Allowable Increase

Allowable Decrease

0.25

0.114

2.75

Answer: The optimal product mix calls for 55 Nacholupas to be prepared at a sale price of $2.75. This amount of Nacholupas would be optimal if the price rose by 25 cents up to $3 or dropped by 11.4 cents down to $2.636. Diff: 2 Page Ref: 118 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking

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62) The assistant manager had taken a management science class a few years before and while she knew enough to formulate the problem and implement it in Excel, the only sensitivity training she had ever received had to do with being more empathetic to the plight of her minimum wage workforce. Help her interpret the sensitivity report for the cheese and meat constraints as it appears below.

Cell $G$7 $G$8

Name

Final Shadow Constraint Value Price R.H. Side

Cheese Meat

400 150

0.25 0.125

Allowable Increase

Allowable Decrease

16.66666667 110

233.3333333 10

400 150

Answer: All 400 ounces of the cheese and 150 ounces of the meat are used in the optimal product mix. If the assistant manager could buy an ounce of cheese for 25 cents or less, they should do that up to an additional 16.6 ounces of cheese. If they were to waste cheese, each ounce lost would effectively lose them 25 cents up to losing 233 ounces. Additional meat should be purchased up to a price of 12.5 cents per ounce and up to an additional 110 ounces. Wasting an ounce of meat costs 12.5 cents per ounce up to a loss of 10 ounces. Diff: 2 Page Ref: 118 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking

63) When systematically formulating a linear program, the first step is to: A) construct the objective function. B) formulate the constraints. C) identify the decision variables. D) identify the parameter values. Answer: C Diff: 2 Page Ref: 115 Section Heading: A Product Mix Example Keywords: formulation AACSB: Application of knowledge

64) Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock 2". The constraint for this requirement can be written as: A) x2 ≥ .60. B) x2 ≥ .60 (x2 + x7 + x8). C) .4x2 - .6x7 - .6x8 ≤ 0. D) .4x2 - .6x7 - .6x8 ≥ 0. Answer: C Diff: 3 Page Ref: 122-127 Section Heading: An Investment Example Keywords: formulation AACSB: Analytical thinking

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65) The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B, which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. Minimum daily Percent per pound Percent per pound requirement Ingredient in Feed A in Feed B (pounds) 1 20 24 30 2 30 10 50 3 0 30 20 4 24 15 60 5 10 20 40 The constraint for ingredient 3 is: A) .5A + .75B = 20. B) .3B = 20. C) .3B≤ 20. D) .3B ≥ 20. Answer: D Diff: 2 Page Ref: 119-122 Section Heading: A Diet Example Keywords: solution AACSB: Analytical thinking

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50. 66) For the production combination of 800 bags of lime and 600 bags of vinegar, which of the three resources is (are) not completely used? A) flour only B) salt only C) herbs only D) salt and flour Answer: B Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: solution, slack AACSB: Analytical thinking

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67) What is the constraint for salt? A) 6L + 8V ≤ 4800 B) 1L + 2V ≤ 4800 C) 3L + 2V ≤ 4800 D) 2L + 3V ≤ 4800 Answer: D Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: formulation, constraints AACSB: Analytical thinking

68) Which of the following is not a feasible production combination? A) 0L and 0V B) 0L and 1000V C) 1000L and 0V D) 0L and 1200V Answer: D Diff: 1 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: formulation, feasibility AACSB: Analytical thinking

Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. 69) What is an appropriate objective function for this fast food vignette? A) Max Z = 2.75N + 4B + 2Q + 3E B) Min Z = 400C + 150M + 400B + 250T C) Min Z = 2.75N + 4B + 2Q + 3E D) Max Z = 400C + 150M + 400B + 250T Answer: A Diff: 1 Page Ref: 116 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking

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70) Which of these is a decision variable for the LP formulation of this problem? A) cheese B) Nacholupa C) 400 D) $2.75 Answer: B Diff: 1 Page Ref: 115 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking

71) What is an appropriate constraint for this fast food vignette? A) 250T + 400B + 150M + 400C B) 4C + 1M + 0B + 4T ≤ 4 C) 2N + 4B + 4Q + 3E ≤ 400 D) 2.75N + 4B + 2Q + 3E Answer: C Diff: 1 Page Ref: 116 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking

72) How many decision variables are in the LP formulation? A) 1 B) 2 C) 3 D) 4 Answer: D Diff: 1 Page Ref: 115 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking

73) Which of these statements about the sensitivity report is best?

Cell

Name

$D$4 $C$4

Burritaco Nacholupa

Final Reduced Objective Value Cost Coefficient 0 55

-0.125 0

Allowable Increase

Allowable Decrease

0.125 0.25

1E+30 0.114

4 2.75

A) There are no Burritacos being made. B) If the Nacholupa has a cost reduction of more than 0, none will be made. C) The company can make up to 1E+30 Burritacos. D) The company can make an additional 0.25 Nacholupas if they want to with the leftover ingredients. Answer: A Diff: 1 Page Ref: 116-118 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking

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74) Which of the statements about this portion of the sensitivity report is best?

Cell $G$7 $G$8

Name Cheese Meat

Final Shadow Constraint Value Price R.H. Side 400 150

0.25 0.125

Allowable Increase

Allowable Decrease

16.66666667 110

233.3333333 10

400 150

A) Cheese costs more than meat. B) One additional pound of meat should be purchased if it can be acquired for $2 or less. C) There is both cheese and meat left over if the optimal product mix is produced. D) The shadow price of cheese can rise to 16.8167 before the right hand side changes. Answer: B Diff: 1 Page Ref: 116-118 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking

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Exposure 5,000 3,000 700 200

Cost $500 $250 $25 $15

The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) 75) What is an appropriate objective function for this scenario? A) Max Z = 5,000N + 3,000R + 700T + 200F B) Max Z = 500N + 250R + 125T + 15F C) Min Z = 500N + 250R + 125T + 15F D) Min Z = 5,000N + 3,000R + 700T + 200F Answer: A Diff: 1 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking

76) Which of these is an appropriate constraint for this scenario? A) 5,000N + 3,000R + 700T + 200F ≤ 3,500 B) 500N + 250R + 125T + 15F ≤ 3,500 C) N + R + T + F ≥ 36 D) T ≤ 2,800 Answer: B Diff: 1 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking

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77) A portion of the variable cells section of the sensitivity report in Excel appears in the table below. How many potential customers will be reached by the optimal advertising campaign?

Cell

Name

$C$2 $D$2 $E$2 $F$2

Newspaper Radio Twitter Facebook

Final Reduced Objective Value Cost Coefficient 0 13.76 0 4

-1000 0 -800 0

5000 3000 700 200

A) 17.76 B) 8,900 C) 42,080 D) cannot be determined from the sensitivity report Answer: C Diff: 1 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking

78) Which of these statements about the sensitivity report for the constraints is best?

Cell

Name

Final Shadow Constraint Value Price R.H. Side

$G$5

Budget

3500

Allowable Increase

Allowable Decrease

2560

3440

A) Only $940 of the advertising budget is being spent on this campaign. B) The advertising campaign needs another $2,560 to reach the maximum number of customers. C) It is possible to reach enough customers by spending only $60. D) For every $1 increase in the budget, the ad campaign can reach twelve more customers. Answer: D Diff: 1 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking

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79) What is the proper interpretation of the shadow price for Facebook?

Cell

Name

$G$9

Facebook

Final Shadow Constraint Value Price R.H. Side 4

Allowable Increase

229.3333333

Allowable Decrease 4

A) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 233. B) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 229. C) If they spend $4, then can reach 20 customers. D) If they spend less than $20, they can reach 229.333 customers. Answer: A Diff: 1 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking

80) How should the entry for the Newspaper decision variable be interpreted?

Cell

Name

$C$2

Newspaper

Final Reduced Objective Value Cost Coefficient 0

-1000

5000

Allowable Increase

Allowable Decrease

1000

1E+30

A) The director should lower the newspaper advertising expense by $1,000 to reach the objective of 5,000 customers contacted. B) If the director were forced to purchase a newspaper advertisement, he would reach 1000 fewer customers than would be reached using the optimal advertising campaign. C) If the director increased newspaper advertisement by 1,000, he would spend $1000 less than with the current campaign. D) It is possible to reach an almost infinite fewer number (10 to the 30th power) of customers by newspaper than by any other method. Answer: B Diff: 1 Page Ref: 128-131 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking

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81) If Xab = the production of product a in period b, then to indicate that the limit on production of the company's 3 products in period 2 is 400, we write: A) X32 ≤ 400. B) X21 + X22 + X23 ≤ 400. C) X12 + X22 + X32 ≤ 400. D) X12 + X22 + X32 ≥ 400. Answer: C Diff: 2 Page Ref: 139-144 Section Heading: A Multiperiod Scheduling Example Keywords: formulation, constraints AACSB: Analytical thinking

82) Balanced transportation problems have which of the following type of constraints? A) ≥ B) ≤ C) = D) < Answer: C Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: formulation, constraints AACSB: Application of knowledge

83) Compared to blending and product mix problems, transportation problems are unique because: A) they maximize profit. B) the constraints are all equality constraints with no "≤" or "≥" constraints. C) they contain fewer variables. D) the solution values are always integers. Answer: D Diff: 2 Page Ref: 132-134 Section Heading: A Transportation Example Keywords: transportation AACSB: Application of knowledge

26 .

84) A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit? A) $380 B) $400 C) $420 D) $440 Answer: A Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: computer solution AACSB: Analytical thinking

27 .

Leghorn 5 3 2 3 5

Cochin 2 9 8 2 4

Buff Orpington 4.5 6 5 4 8

Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. 85) Which of the following is an appropriate objective function? A) Max Z = 5L + 2C + 4.5B B) Max Z = 10L + 10C + 10B C) Min Z = 5L + 2C + 4.5B D) Min Z = 10L + 10C + 10B Answer: A Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: objective, cost minimization, profit maximization AACSB: Analytical thinking

86) The poultry farmer would like to generate 80 ounces of fertilizer per week while feeding a maximum of 160 ounces of layer pellets each week. Which of these constraints is correct? A) 3L + 2C + 4C ≤ 80 B) 5L + 4C + 8B ≤ 160 C) 5L + 4C + 8B ≥ 160 D) 5L + 4C +8B ≥ 80 Answer: B Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: constraint, model formulation AACSB: Analytical thinking

28 .

87) The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. When he runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He can picture the sad little faces of his children when he tells them that there will be no variety of birds gracing their front lawn this summer. Help him avoid the embarrassment by selecting a constraint that will ensure that there is some variety in his flock. A) 5L + 4C + 8B ≤ 160 B) 5L + 4C + 8B ≥ 160 C) C + B ≥ 5 D) L + C + B ≥ 5 Answer: C Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: constraints, formulation AACSB: Analytical thinking

88) When the poultry farmer runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He studies his sensitivity report (copied below) and decides to write a constraint that requires two Cochin chickens to be selected. If the current optimal mix of breeds results in 160 eggs per week, which of the following statements is best?

Cell $B$1 $C$1 $D$1

Objective Coefficient 5 2 4.5

Name Final Value Reduced Cost Leghorn 32 0 Cochin 0 -2 Buff Orpington 0 -3.5

A) The new weekly egg output will be 169. B) The new weekly egg output will be 162. C) The new weekly egg output will be 158. D) The new weekly egg output will be 153. Answer: D Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: constraint, model formulation AACSB: Analytical thinking

29 .

Allowable Increase 1E+30 3 3.5

Allowable Decrease 2.1875 1E+30 1E+30

89) The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. Use this portion of the sensitivity report to evaluate the following statements:

Cell $B$1 $C$1 $D$1

Name Final Value Reduced Cost Leghorn 32 0 Cochin 0 -2 Buff Orpington 0 -3.5

Objective Coefficient 5 2 4.5

Allowable Increase 1E+30 3 3.5

Allowable Decrease 2.1875 1E+30 1E+30

A) The noise level around the farm should be over 60 decibels. B) The fertilizer generated will be 160 ounces per week. C) Layer pellets will be consumed at the rate of 96 ounces per week. D) The plumage score will be less than 40. Answer: A Diff: 2 Page Ref: 114-118 Section Heading: A Product Mix Example Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking

90) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component 1. A) x21 + x22 ≤ 8000 B) x12 + x22 ≥ 8000 C) x11 + x12 ≤ 8000 D) x21 + x22 ≥ 8000 Answer: C Diff: 2 Page Ref: 135-138 Section Heading: A Blend Example Keywords: formulation AACSB: Analytical thinking

91) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the demand constraint for gasoline type 1. A) x21 + x22 = 11000 B) x12 + x22 = 11000 C) x11 + x21 ≤ 11000 D) x11 + x21 = 11000 Answer: D Diff: 2 Page Ref: 135-138 Section Heading: A Blend Example Keywords: formulation AACSB: Analytical thinking

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92) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1. A) x11 + x12 (.35)(x11 + x21) B) x11 + .35(x11 + x12) C) -.65x11 + .35x21 ≤ 0 D) .65x11 - .35x21 ≤ 0 Answer: D Diff: 3 Page Ref: 135-138 Section Heading: A Blend Example Keywords: formulation AACSB: Analytical thinking

93) Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil-base and water-base paint. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oilbase paint, and y represents the gallons of water-base paint, which constraint is correctly represents the constraint on ingredient A? A) .9A + .1B ≤ 10,000 B) .9x + .1y ≤ 10,000 C) .3x + .7y ≤ 10,000 D) .9x + .3y ≤ 10,000 Answer: D Diff: 2 Page Ref: 135-138 Section Heading: A Blend Example Keywords: blend AACSB: Analytical thinking

94) A systematic approach to model formulation is to first: A) construct the objective function . B) develop each constraint separately. C) define decision variables. D) determine the right hand side of each constraint. Answer: C Diff: 2 Page Ref: 115 Section Heading: A Product Mix Example Keywords: model formulation AACSB: Application of knowledge

31 .

95) Let: rj = regular production quantity for period j, oj =overtime production quantity in period j, ij = inventory quantity in period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is: A) rj + oj + i2 - i1 ≥ dj. B) rj + oj + i1 - i2 ≥ dj. C) rj + oj + i1 - i2 ≤ dj. D) rj - oj - i1 + i2 ≥ dj. Answer: A Diff: 2 Page Ref: 139-144 Section Heading: A Multiperiod Scheduling Example Keywords: formulation, constraints AACSB: Analytical thinking

96) In a multiperiod scheduling problem, the production constraint usually takes the form of: A) beginning inventory + demand - production = ending inventory. B) beginning inventory - demand + production = ending inventory. C) beginning inventory - ending inventory + demand = production. D) beginning inventory + demand + production = ending inventory. Answer: B Diff: 2 Page Ref: 139-144 Section Heading: A Multiperiod Scheduling Example Keywords: model formulation, multi-period scheduling problem AACSB: Analytical thinking

97) The type of linear program that compares services to indicate which one is less productive or inefficient is called: A) product mix. B) data envelopment analysis. C) marketing. D) blending. Answer: B Diff: 2 Page Ref: 144 Section Heading: A Data Envelopment Analysis Example Keywords: formulation AACSB: Application of knowledge

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In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. 98) The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint? A) X2 ≤ 10000 X2 + X3 ≤ 350 B) 10,000 X2 ≤ 350X2 + 350X3 C) 47.25X2 ≤ 10,000 X2 + X3 ≤ 350 D) 47.25X2 ≤ 10,000 47.25 X2 + 110X3 ≤ 350 Answer: C Diff: 2 Page Ref: 122-127 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking

99) An appropriate part of the model would be: A) 15X1 + 47.25X2 + 110 X3 ≤ 50,000. B) MAX 15X1 + 47.25X2 + 110X3. C) X1 + X2 +X3 ≤ 50,000. D) MAX 50(15)X1 + 50 (47.25)X2 + 50 (110)X3. Answer: A Diff: 2 Page Ref: 122-127 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking

100) The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is: A) MAX .06X1 +.08X2 +.11X3. B) MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3. C) MAX 15X1 + 47.25X2 +.110X3. D) MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3. Answer: B Diff: 2 Page Ref: 122-127 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking

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101) The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? A) X1 ≤ 0.35 B) X1 = 0.35 (50000) C) X1 ≤ 0.35(X1 + X2 + X3) D) X1 = 0.35(X1 + X2 + X3) Answer: C Diff: 2 Page Ref: 122-127 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking

34 .

Introduction to Management Science, 12e (Taylor) Chapter 5 Integer Programming 1) The three types of integer programming models are total, 0-1, and mixed. Answer: TRUE Diff: 1 Page Ref: 186 Section Heading: Integer Programming Models Keywords: integer programming models AACSB: Application of knowledge

2) In a total integer model, all decision variables have integer solution values. Answer: TRUE Diff: 1 Page Ref: 186 Section Heading: Integer Programming Models Keywords: integer programming models AACSB: Application of knowledge

3) In a 0-1 integer model, the solution values of the decision variables are 0 or 1. Answer: TRUE Diff: 1 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming models AACSB: Application of knowledge

4) In a mixed integer model, some solution values for decision variables are integer and others can be non-integer. Answer: TRUE Diff: 1 Page Ref: 188 Section Heading: Integer Programming Models Keywords: integer programming models AACSB: Application of knowledge

5) The college dean is deciding among three equally qualified (in their eyes, at least) candidates for his associate dean position. If this situation could be modeled as an integer program, the decision variables would be cast as 0-1 integer variables. Answer: TRUE Diff: 1 Page Ref: 187 Section Heading: Integer Programming Models Keywords: 0-1 variables, conditional constraints AACSB: Analytical thinking

6) The management scientist's fiance informed him that if they were to be married, he would also have to welcome her mother into their home. The management scientist should model this decision as a contingency constraint. Answer: FALSE Diff: 1 Page Ref: 188 Section Heading: Integer Programming Models Keywords: corequisite constraints, 0-1 variables AACSB: Application of knowledge

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7) In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate. Answer: FALSE Diff: 1 Page Ref: 188 Section Heading: Integer Programming Models Keywords: integer linear programming models, 0-1 variables AACSB: Analytical thinking

8) The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible. Answer: TRUE Diff: 1 Page Ref: 190 Section Heading: Integer Programming Graphical Solution Keywords: integer programming graphical solution AACSB: Analytical thinking

9) In a mixed integer model, all decision variables have integer solution values. Answer: FALSE Diff: 2 Page Ref: 188 Section Heading: Integer Programming Models Keywords: integer programming models AACSB: Application of knowledge

10) In a mixed integer model, the solution values of the decision variables are 0 or 1. Answer: FALSE Diff: 2 Page Ref: 188 Section Heading: Integer Programming Models Keywords: integer programming models AACSB: Application of knowledge

11) The branch and bound solution method cannot be applied to 0-1 integer programming problems. Answer: FALSE Diff: 2 Page Ref: 191 Section Heading: Integer Programming Models Keywords: integer programming models, branch and bound method AACSB: Application of knowledge

12) In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. Answer: TRUE Diff: 2 Page Ref: 201 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: capital budgeting, 0-1 variables AACSB: Analytical thinking

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13) In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected. Answer: FALSE Diff: 2 Page Ref: 201 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: capital budgeting, 0-1 variables AACSB: Analytical thinking

14) The divisibility assumption is violated by integer programming. Answer: TRUE Diff: 1 Page Ref: 186 Section Heading: Integer Programming Models Keywords: integer linear programming models, multiple choice constraint AACSB: Analytical thinking

15) One type of constraint in an integer program is a multiple-choice constraint. Answer: TRUE Diff: 1 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer linear programming models, multiple choice constraint AACSB: Application of knowledge

16) A conditional constraint specifies the conditions under which variables are integers or real variables. Answer: FALSE Diff: 1 Page Ref: 188 Section Heading: Integer Programming Models Keywords: integer linear programming models, constraint AACSB: Application of knowledge

17) Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem. Answer: TRUE Diff: 2 Page Ref: 189 Section Heading: Integer Programming Graphical Solution Keywords: integer programming models, graphical solution AACSB: Analytical thinking

18) A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values. Answer: TRUE Diff: 2 Page Ref: 190 Section Heading: Integer Programming Graphical Solution Keywords: integer programming models, graphical solution AACSB: Application of knowledge

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19) Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Answer: FALSE Diff: 2 Page Ref: 190 Section Heading: Integer Programming Graphical Solution Keywords: integer programming models, graphical solution AACSB: Analytical thinking

20) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint. Answer: TRUE Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer linear programming models, 0-1 variables AACSB: Analytical thinking

21) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint. Answer: FALSE Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: 0-1 variables, multiple choice constraint AACSB: Analytical thinking

22) If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint. Answer: FALSE Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: 0-1 variables, conditional constraints AACSB: Analytical thinking

23) If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint. Answer: FALSE Diff: 2 Page Ref: 188 Section Heading: Integer Programming Models Keywords: 0-1 variables, corequisite constraints AACSB: Analytical thinking

24) If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint. Answer: TRUE Diff: 2 Page Ref: 188 Section Heading: Integer Programming Models Keywords: 0-1 variables, multiple choice constraint AACSB: Analytical thinking

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25) In a ________ linear programming model, some of the solution values for the decision variables are required to assume integer values and others can be integer or noninteger. Answer: mixed integer Diff: 1 Page Ref: 188 Section Heading: Integer Programming Models Keywords: integer programming models, mixed integer programming models AACSB: Application of knowledge

26) In a ________ linear programming model, the solution values of the decision variables are zero or one. Answer: 0-1 integer Diff: 1 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming models, 0-1 integer programming models AACSB: Application of knowledge

27) The ________ method is based on the principle that the total set of feasible solutions can be partitioned into smaller subsets of solutions. Answer: branch and bound Diff: 3 Page Ref: 191 Section Heading: Integer Programming Graphical Solution Keywords: branch and bound method AACSB: Application of knowledge

28) "It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a ________ constraint." Answer: contingency or mutually exclusive Diff: 1 Page Ref: 187 Section Heading: Integer Programming Models Keywords: mutually exclusive constraints, 0-1 variables AACSB: Application of knowledge

29) A ________ integer model allows for the possibility that some decision variables are not integers. Answer: mixed Diff: 1 Page Ref: 188 Section Heading: Integer Programming Models Keywords: mixed integer programming problem AACSB: Application of knowledge

30) In choosing four electives from the dazzling array offered by the Decision Sciences Department next semester, the students that had already taken the management science class were able to craft a model using a ________ constraint. Answer: multiple-choice Diff: 1 Page Ref: 187 Section Heading: Integer Programming Models Keywords: multiple choice constraints, 0-1 variables AACSB: Application of knowledge

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31) ________ variables are best suited to be the decision variables when dealing with yes-or-no decisions. Answer: 0-1 Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer linear programming models, 0-1 variables AACSB: Application of knowledge

32) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint. Answer: mutually exclusive Diff: 2 Page Ref: 187 Section Heading: Integer Programming Graphical Solution Keywords: integer linear programming models, 0-1 variables AACSB: Application of knowledge

33) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint. Answer: multiple-choice Diff: 2 Page Ref: 187 Section Heading: Integer Programming Graphical Solution Keywords: 0-1 variables, multiple choice constraint AACSB: Application of knowledge

34) If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. Answer: conditional Diff: 2 Page Ref: 188 Section Heading: Integer Programming Graphical Solution Keywords: 0-1 variables, conditional constraints AACSB: Application of knowledge

35) If one location for a warehouse can be selected only if a specific location for a manufacturing facility is also selected, this decision can be represented by a ________ constraint. Answer: conditional Diff: 2 Page Ref: 188 Section Heading: Integer Programming Models Keywords: integer linear programming models, constraint AACSB: Analytical thinking

36) In an integer program, if we were choosing between two locations to build a facility, this would be written as: ________. Answer: x1 + x2 = 1 Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer linear programming models, constraint AACSB: Analytical thinking

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37) In an integer program, if building one facility required the construction of another type of facility, this would be written as: ________. Answer: x1 = x2 Diff: 2 Page Ref: 188 Section Heading: Integer Programming Models Keywords: integer linear programming models, constraint AACSB: Analytical thinking

38) Consider the following integer linear programming problem: Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 ≤ 30 4x1 + 2x2 ≤ 28 x1 ≤ 8 x1 , x2 ≥ 0 and integer The solution to the linear programming formulation is: x1 = 5.714, x2 = 2.571. What is the optimal solution to the integer linear programming problem? State the optimal values of decision variables and the value of the objective function. Answer: x1 = 6, x2 = 2, Z = 22 Diff: 2 Page Ref: 189 Section Heading: Integer Programming Graphical Solution Keywords: integer linear programming solution AACSB: Analytical thinking

39) Consider the following integer linear programming problem: Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 ≤ 30 5x1 + 2x2 ≤ 28 x1 ≤ 8 x1, x2 ≥ 0 and integer The solution to the linear programming formulation is: x1 = 5.714, x2 = 2.571. What is the optimal solution to the integer linear programming problem? State the optimal values of decision variables and the value of the objective function. Answer: x1 = 4, x2 = 3, Z = 18 Diff: 2 Page Ref: 190 Section Heading: Integer Programming Graphical Solution Keywords: integer linear programming solution AACSB: Analytical thinking

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Consider a capital budgeting example with five projects from which to select. Let x1 = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300, respectively. The budget is $450. 40) Write the appropriate constraint for the following condition: Choose no fewer than 3 projects. Answer: x1 + x2 + x3 + x4 + x5 ≥ 3 Diff: 1 Page Ref: 201 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: formulation of 0-1 constraints AACSB: Analytical thinking

41) Write the appropriate constraint for the following condition: If project 3 is chosen, project 4 must be chosen. Answer: x3 - x4 ≤ 0 Diff: 1 Page Ref: 187 Section Heading: Integer Programming Models Keywords: formulation of 0-1 constraints AACSB: Analytical thinking

42) Write the appropriate constraint for the following condition: If project 1 is chosen, project 5 must not be chosen. Answer: x1 + x5 ≤ 1 Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: formulation of 0-1 constraints AACSB: Analytical thinking

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The Deadbeats After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door — you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. 43) Formulate an appropriate objective function for this scenario. Answer: If the variables are assigned as in the table: x1 = contractor works on wood floors

x2 = landlord works on wood floors

x3 = contractor works on kitchen tile

x4 = contractor works on kitchen tile

x5 = contractor works on back door

x6 = contractor works on back door

x7 = contractor works on garage door

x8 = contractor works on garage door

then an appropriate objective function will be: Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, 0-1 integer programming AACSB: Analytical thinking

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44) Formulate an appropriate model for this scenario. Answer: If the variables are assigned as in the table: x1 = contractor works on wood floors

x2 = landlord works on wood floors

x3 = contractor works on kitchen tile

x4 = contractor works on kitchen tile

x5 = contractor works on back door

x6 = contractor works on back door

x7 = contractor works on garage door

x8 = contractor works on garage door

then an appropriate objective function will be: Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 Subject to: x1 + x 2 ≤ 1 x3 + x 4 ≤ 1 x5 + x 6 ≤ 1 x7 + x 8 ≤ 1 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6 , x7, x8 are 0,1 Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, 0-1 integer programming AACSB: Analytical thinking

45) Formulate an appropriate model for this scenario if the variables are assigned as in the table: x1 = contractor works on wood floors

x2 = landlord works on wood floors

x3 = contractor works on kitchen tile

x4 = contractor works on kitchen tile

x5 = contractor works on back door

x6 = contractor works on back door

x7 = contractor works on garage door

x8 = contractor works on garage door

Answer: Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 Subject to: x1 + x 2 ≤ 1 x3 + x 4 ≤ 1 x5 + x 6 ≤ 1 x7 + x 8 ≤ 1 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6 , x7, x8 are 0,1 Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, 0-1 integer programming AACSB: Analytical thinking

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46) I know it's hard to believe that his job as a management scientist doesn't comfortably keep him in Ferraris and caviar, but the insurance premiums on his ride are outrageous, and frankly it doesn't get good gas mileage in the city. Hence, the management scientist/landlord runs his model and receives this output. Provide an interpretation of exactly what will happen in the coming weeks. Cell

Name

Original Value

Final Value

Integer

$G$4 $H$4 $G$5 $H$5 $G$6 $H$6 $G$7 $H$7

wood floors contractor wood floors landlord kitchen tile contractor kitchen tile landlord back door contractor back door landlord garage door opener contractor garage door opener landlord

1 1 1 1 1 1 1 1

0 1 1 0 0 0 0 0

Binary Binary Binary Binary Binary Binary Binary Binary

Answer: It appears that the landlord/management scientist will tackle the wood floors himself and have a contractor install kitchen tile. This will take 3.5 weeks, leaving one half week free, and will cost $2900 out of the maximum $3,000 budget, leaving $100 — enough for beer and pizza, or at least pizza. It is somewhat ambiguous whether the landlord has four weeks to work with and the contractors have four weeks or whether the entire model's time constraint should have only four weeks - if we knew whether there were wood floors in the kitchen and two work groups would get in each other's way, then we could set up constraints to capture this situation. Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, 0-1 integer programming AACSB: Analytical thinking

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47) The management scientist was planning to leave his actions up to the wisdom of his model, but before he could press "Solve" on his Excel spreadsheet, his wife weighed in on the project. This was only reasonable, as it was her house before they tied the knot. It has been her dream to move back into this cottage once the management scientist goes to his great reward. She insists that the back door and garage door components of this project happen. If the variables have been chosen as in the table, construct an objective function and constraints that meet the management scientist's bride's requests. x1 = contractor works on wood floors

x2 = landlord works on wood floors

x3 = contractor works on kitchen tile

x4 = contractor works on kitchen tile

x5 = contractor works on back door

x6 = contractor works on back door

x7 = contractor works on garage door

x8 = contractor works on garage door

Answer: Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 Subject to: x1 + x 2 ≤ 1 x3 + x 4 ≤ 1 x5 + x 6 = 1 x7 + x 8 = 1 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6 , x7, x8 are 0,1 Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, 0-1 integer programming AACSB: Analytical thinking

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48) The management scientist was planning to leave his actions up to the wisdom of his model, but before he could press "Solve" on his Excel spreadsheet, his wife weighed in on the project. This was only reasonable, as it was her house before they tied the knot. It has been her dream to move back into this cottage once the management scientist goes to his great reward. She insists that the back door and garage door components of this project happen. After making these changes, the management scientist ran the model and obtained the following answer report. Provide a full interpretation. Variable Cells Cell

Name

Original Value

Final Value

Integer

$G$4 $H$4 $G$5 $H$5 $G$6 $H$6 $G$7 $H$7

wood floors Contractor? wood floors Landlord? kitchen tile Contractor? kitchen tile Landlord? back door Contractor? back door Landlord? garage door opener Contractor? garage door opener Landlord?

0 1 1 0 0 0 0 0

0 1 0 0 1 0 1 0

Binary Binary Binary Binary Binary Binary Binary Binary

Constraints Cell $B$12 $E$10 $I$4 $I$5 $I$6

Name

Total Time Weeks Total Cost wood floors Included kitchen tile Included back door Included gar door open $I$7 Included $G$4:$H$7= Binary

Cell Value

Formula

2.75 $1,350 1 0 1

Status

$B$12<=$B$13 Not Binding $E$10<=$E$11 Not Binding $I$4<=$J$4 Binding $I$5<=$J$5 Not Binding $I$6=$J$6 Binding

$I$7=$J$7

Binding

Slack 1.25 1650 0 1 0 0

Answer: The landlord will be refinishing the wood floors and the contractor(s) will be tackling the garage door opener and back door installations. those projects will cost a total of $1350, leaving $1650 left in the budget. These projects will take 2.75 weeks out of the four weeks available. The landlord should be able to increase the monthly rent by $135 once these upgrades have been completed. The only upgrade not completed will be the kitchen tile. Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, 0-1 integer programming AACSB: Analytical thinking

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49) The management scientist entered a trance-like state as he formulated his model. This state was interrupted by an integer-hating colleague, who insisted that the model should be run as a linear program rather than integer program. The management scientist sighed, relaxed the integer constraint, and ran the model, obtaining the following answer report. Provide a full interpretation and plan for action. Variable Cells Cell

Name

$G$4 $H$4 $G$5 $H$5 $G$6 $H$6 $G$7 $H$7

wood floors Contractor? wood floors Landlord? kitchen tile Contractor? kitchen tile Landlord? back door Contractor? back door Landlord? garage door opener Contractor? garage door opener Landlord?

Original Value Final Value 0 0 0 0 0 0 0 0

0 1 0.833 0.167 0.000 0 1 0

Integer Contin Contin Contin Contin Contin Contin Contin Contin

Constraints Cell

Name

$B$12 Total Time Weeks Contractor $E$10 Total Cost Contractor Price $I$4 wood floors Included? $I$5 kitchen tile Included? $I$6 back door Included? $I$7 garage door opener Included?

Cell Value 4 $3,000 1 1 2.78E-16 1

Formula

Status

$B$12<=$B$13 Binding $E$10<=$E$11 Binding $I$4<=$J$4 Binding $I$5<=$J$5 Binding $I$6<=$J$6 Not Binding $I$7<=$J$7 Binding

Slack 0 0 0 0 1 0

Answer: The landlord uses the entire budget, takes the entire four weeks and installs (or has the contractor install) the floors, garage door, and the kitchen tile, leaving only the back door off the improvement list. The kitchen tile project is split between the landlord, who does one-sixth of the work, and the contractor, who completes the remaining five-sixths. Although the model meets the constraints, this is not a practical solution in the real world. The management scientist should realize that moving to an integer solution within the LP feasible region will result in a feasible solution, albeit one with no guarantee of optimality. If the integer solution of wood floors and the garage door is chosen, there would be money and time both left over in the project budget, but the management scientist should reintroduce the integer constraint to confirm the best choice of action. Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, 0-1 integer programming AACSB: Analytical thinking

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The Cruise Their cruise would port out of New Orleans and promised seven days with a panoply of excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site and key features of each appear in the table. The excursions were all day affairs, so it was possible to engage in only one per port. The cruise ship sailed at night and docked at each of these three ports at the crack of dawn. By dinner time, the ship was on its way to the next port and next set of excursions. The couple was energetic and active for a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't want to spend money on excursions that might be better spent on tacky souvenirs. The couple therefore budgeted $250 for the excursions — the prices shown are per couple, so for example, the $60 will pay for both of them to fill up on jerk chicken and mannish water. For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the couple researched the quality of the activity and ranked the excursion among the available alternatives, with higher numbers indicating better quality. Thus, snorkeling in Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3. Site Rating Activity Cost Jamaica 3 snorkeling $100 Jamaica 1 party island $95 Jamaica 2 horseback ride $120 Jamaica 3 local cuisine $60 Cozumel 2 snorkeling $110 Cozumel 3 party island $55 Cozumel 1 horseback ride $70 Cozumel 2 local cuisine $90 Cozumel 3 tequila tasting $130 Grand Cayman 1 snorkeling $90 Grand Cayman 2 party island $60 Grand Cayman 3 horseback ride $110 Grand Cayman 1 local cuisine $130 Grand Cayman 3 turtle farm $95 (Note - data used in this test question should not be construed as vacation advice.) 50) What is an appropriate objective function for this vacation? Answer: Using the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), the objective function should be expressed as: Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu Diff: 1 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

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51) What is an appropriate objective function and constraints for this vacation? Answer: Using the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), the model should be expressed as: Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu subject to: 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu <= 250 JS + JP + JH + JL ≤ 1 CS + CP + CH + CL + CTe ≤ 1 GS + GP + GH + GL + GTu ≤ 1 JS + CS + GS ≤ 1 JP + CP + GP <= 1 JH + CH + GH <= 1 JL + CL + GL <= 1 JS, JP, JH, JL, CS, CP, CH, CL, CTe, GS, GP, GH, GL, GTu are 0,1 Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

52) The vacationing management scientist sat down at his computer keyboard, cracked his knuckles and decided on the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), for his decision variables. He wrote constraints that read: JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3 JS + JP + JH + JL ≤ 1 CS + CP + CH + CL + CTe≤1 GS + GP + GH + GL + GTu ≤ 1 What do these constraints accomplish in the model and which ones are necessary? Answer: The first constraint limits the total number of excursions to 3. JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3 The second through the fourth constraints limit the excursions at each one of the ports to 1. JS + JP + JH + JL ≤ 1 CS + CP + CH + CL + CTe ≤ 1 GS + GP + GH + GL + GTu ≤ 1 The first constraint doesn't help the model and can be eliminated. If it were used in place of constraints 2 through 4, the model might suggest taking all three excursions at one port of call, which would be impossible. Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

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53) The first day on the cruise was a "day at sea" meaning no port of call, and only the amenities onboard for amusement. Restless and uncomfortably full after seven trips through the buffet, the management scientist gambled away most of his vacation money at the onboard casino. The excursions would be a necessity, but now it became less important to maximize the joy of the excursions and more vital to get off the boat as cheaply as possible while still staying busy at the three pots of call. What is an appropriate objective function for this modified cruise vacation? Answer: Using the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), the objective function should be expressed as: Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu Diff: 1 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

54) The first day on the cruise was a "day at sea" meaning no port of call, and only the amenities onboard for amusement. Restless and uncomfortably full after seven trips through the buffet, the management scientist gambled away most of his vacation money at the onboard casino. The excursions would be a necessity, but now it became less important to maximize the joy of the excursions and more vital to get off the boat as cheaply as possible while still staying busy at the three ports of call. What is an appropriate model for this modified cruise vacation? Answer: Using the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), the objective function should be expressed as: Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu subject to: 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu ≤ 250 JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1 JS + CS + GS ≤ 1 JP + CP + GP ≤1 JH + CH + GH ≤1 JL + CL + GL ≤1 JS, JP, JH, JL, CS, CP, CH, CL, CTe, GS, GP, GH, GL, GTu are 0,1 Diff: 1 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

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Saba conducts regular tours of his favorite city in the world, Paris. Each semester he selects among the finest students in the university and escorts them to the City of Lights. In addition to a world-class education on conducting business in Europe, he arranges a number of cultural outings for them to help them immerse themselves in all that France has to offer. He collects an extra $100 from each student for this purpose and limits his tour group to ten lucky individuals. Some of the events (and their prices) he proposes to the students include: Eiffel Tower visit, $40 per student, E Paris Sewer spelunking, $20 per student, S Half day passes to the Louvre, $60 per student, L Bon Beret tour, $50 per student, B So much to do and so little time! 55) What would the constraints be if the Eiffel Tower visit needed to take place at the same time as the half day at the Louvre and if students taking the Paris Sewer tour had to wear the special sanitary beret available only from the Bon Beret tour? Answer: E + L ≤ 1 S-B≤0 Diff: 2 Page Ref: 200-209 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: mutually exclusive constraints, 0-1 variables AACSB: Analytical thinking

56) The tour group has three days remaining in Paris and the opportunity to do three cultural events. It is important to soak up as much culture as possible, so Saba decides to model this as a 0-1 integer program mandating that the group does three events. A couple of students object, not to the integer program, but to the set of cultural events that they have to choose from. They would rather have the option to do up to three events but perhaps only one or two and spend the rest of their time doing some "retail benchmarking." What was Saba's original constraint and how does that constraint change to cater to the whims of the students? Answer: Saba's original constraint was E + L + S + B = 3, which directed the group to three tours. The new constraint is E + L + S + B ≤ 3, which allows for the possibility of no tours up to a maximum of three tours. Diff: 1 Page Ref: 200-209 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: 0-1 variables, multiple choice constraint AACSB: Analytical thinking

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57) What is the full set of constraints if the following situations occur? The Eiffel Tower visit needed to take place at the same time has the half day at the Louvre. Students taking the Paris Sewer tour had to wear the special sanitary beret available only from the Bon Beret tour. Saba applies for university travel funds and supplements the students' accounts with an extra $30 each. Answer: E + L ≤ 1 S-B≤0 40E + 20S + 60L + 50B ≤ 130 Diff: 2 Page Ref: 200-209 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: mixed integer programming problem, constraint formulation AACSB: Analytical thinking

The Exorbitant Course Fees. The $75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of $56,250 in its first semester. "Now we just need to make sure we spend it all," the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use. Decision Variable A B C D E

Item Cost iPads for everybody $750/unit iPad covers with MBA logo $25/unit Speaker series $15,000 Subscriptions to the Wall Street Journal $10/unit Subscriptions to the electronic version of the Wall Street Journal $5/unit

Note Must get a cover if these are purchased Not needed unless we buy iPads Can't afford both this and the iPads Don't need if we have the electronic version Worthless without the iPads

58) What is a full set of constraints for this problem if there are 30 MBA students enrolled this semester? Answer: 22,500A + 750B + 15,000C + 300D + 150E ≤ 56,250 A+C≤1 A-B=0 E-A≤0 D+E≤1 Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer linear programming models, 0-1 variables AACSB: Analytical thinking

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The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

59) This problem requires two different kinds of decision variables. Clearly define each kind. Answer: xa = the number of hoses produced on machine a; ya = 1 if machine a is used, 0 if not Diff: 2 Page Ref: 201 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer program prob formulation, decision variable definition AACSB: Analytical thinking

60) Write the objective function. Answer: MIN Z = 1.25X1 + 1.50X2 + 1.00X3 + 2.000X4+ 750Y1 + 500Y2 +1000Y3 + 300Y4 Diff: 2 Page Ref: 201 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming problem formulation, model constraints AACSB: Analytical thinking

61) Write a constraint to ensure that if machine 4 is used, then machine 1 will not be used. Answer: y1 + y4 ≤ 1 Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming problem formulation, model constraints AACSB: Analytical thinking

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62) Write a constraint that will ensure that Weithoff purchases exactly two machines. Answer: Y1 + Y2 + Y3 + Y4 = 2 Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming formulation, constraint AACSB: Analytical thinking

63) Max Z = x1 + 6x2 Subject to:

17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer

Find the optimal solution. Answer: x1 = 0, x2 = 9, Z = 54 Diff: 2 Page Ref: 191-199 Section Heading: Computer Solution of Integer Program Probs w/Excel, QM for Win Keywords: integer programming problem computer solution AACSB: Analytical thinking

64) Max Z = 3x1 + 5x2 Subject to:

7x1 + 12x2 ≤ 136 3x1 + 5x2 ≤ 36 x1, x2 ≥ 0 and integer

Find the optimal solution. Answer: x1 = 12, x2 = 0, Z = 36 Diff: 2 Page Ref: 191-199 Section Heading: Computer Solution of Integer Program Probs w/Excel, QM for Win Keywords: integer programming problem computer solution AACSB: Analytical thinking

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65) Solve the following integer linear program graphically. MAX Z =

5x1 + 8x2

s.t.

x1 + x2 ≤ 6 5x1 + 9x2 ≤ 45 x1, x2 ≥ 0 and integer

Answer: x1 = 0, x2 = 5, Z = 40 Note that feasible space lattice points have been shaded.

Diff: 3 Page Ref: 191-199 Section Heading: Computer Solution of Integer Program Probs w/Excel, QM for Win Keywords: integer programming graphical solution AACSB: Analytical thinking

66) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint for the first restriction. Answer: S1 + S3 + S7 ≤ 2 Diff: 3 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming formulation, constraint AACSB: Analytical thinking

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67) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint(s) for the second restriction. Answer: S2 + S5 ≤ 1, S4 + S5 ≤ 1 Diff: 3 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming formulation, constraint AACSB: Analytical thinking

68) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint for the third restriction. Answer: S1 + S2 + S3 +S4 + S5 + S6 + S7 ≥ 3 Diff: 1 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming formulation, constraint AACSB: Analytical thinking

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Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region.

DC 1 2 3

A 1 2 3

Region B C 3 3 4 1 2 2

D 2 3 3

The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. 69) Define the decision variables for this situation. Answer: y1 = 1 if DC1 is selected, 0 otherwise y2 = 1 if DC2 is selected, 0 otherwise y3 = 1 if DC3 is selected, 0 otherwise x1A = quantity shipped from DC 1 to Region A x1B = quantity shipped from DC 1 to Region B x1C = quantity shipped from DC 1 to Region C x1D = quantity shipped from DC 1 to Region D x2A = quantity shipped from DC 2 to Region A x2B = quantity shipped from DC 2 to Region B x2C = quantity shipped from DC 2 to Region C x2D = quantity shipped from DC 2 to Region D x3A = quantity shipped from DC 3 to Region A x3B = quantity shipped from DC 3 to Region B x3C = quantity shipped from DC 3 to Region C x3D = quantity shipped from DC 3 to Region D Diff: 2 Page Ref: 203-204 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: facility location example, mixed integer programming AACSB: Analytical thinking

70) Write the objective function for this problem. Answer: Min Z = 1x1A + 3x1B + 3x1C + 2x1D + 2x2A + 4x2B + 1x2C + 3x2D + 3x3A + 2x3B + 2x3C +3x3D + 500y1 + 600y2 + 525y3 Diff: 2 Page Ref: 204 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: facility location example, mixed integer programming AACSB: Analytical thinking

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71) Write the constraints for the three distribution centers. Answer: x1A + x1B +x1C - 500y1 ≤ 0 x2A + x2B +x2C - 500y2 ≤ 0 x3A + x3B +x3C - 500y3 ≤ 0 Diff: 2 Page Ref: 204 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: facility location example, mixed integer programming AACSB: Analytical thinking

The Deadbeats After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door — you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. 72) Obviously if the model wants to upgrade the kitchen, it should be done by either the landlord or a subcontractor. As he creates the IP model, the landlord wants to leave the choice of whether to actually upgrade the kitchen up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables? x1 = contractor works on wood floors

x2 = landlord works on wood floors

x3 = contractor works on kitchen tile

x4 = contractor works on kitchen tile

x5 = contractor works on back door

x6 = contractor works on back door

x7 = contractor works on garage door

x8 = contractor works on garage door

A) x3 + x4 ≤ 1 B) x3 + x4 = 1 C) x3 - x4 ≤ 1 D) x3 - x4 = 1 Answer: A Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

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73) Suppose the landlord really wants the back door to be installed. For too long he has had to cut through the garage and he figures when he retires, this house will be a perfect downsize home for him to move into. How should the constraint for the back door be written if he uses the following scheme for decision variables? x1 = contractor works on wood floors

x2 = landlord works on wood floors

x3 = contractor works on kitchen tile

x4 = contractor works on kitchen tile

x5 = contractor works on back door

x6 = contractor works on back door

x7 = contractor works on garage door

x8 = contractor works on garage door

A) x5 + x6 ≤ 1 B) x5 + x6 = 1 C) x5 - x6 ≤ 1 D) x5 - x6 = 1 Answer: B Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

74) The landlord uses the following scheme for decision variables: x1 = contractor works on wood floors

x2 = landlord works on wood floors

x3 = contractor works on kitchen tile

x4 = contractor works on kitchen tile

x5 = contractor works on back door

x6 = contractor works on back door

x7 = contractor works on garage door

x8 = contractor works on garage door

What should the objective function be? A) Min Z = 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 B) Min Z = 2700x1 - 400x2 + 2500x3 - 1000x4 + 600x5 - 250x6 + 350x7 - 400x8 C) Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 D) Max Z = 100x1 - 100x2 + 80x3 - 80x4 + 15x5 - 15x6 + 20x7 - 20x8 Answer: C Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

26 .

75) The landlord uses the following scheme for decision variables: x1 = contractor works on wood floors

x2 = landlord works on wood floors

x3 = contractor works on kitchen tile

x4 = contractor works on kitchen tile

x5 = contractor works on back door

x6 = contractor works on back door

x7 = contractor works on garage door

x8 = contractor works on garage door

Which of these constraints would not be appropriate for this scenario? A) 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 B) 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 C) x3 + x4 = 1 D) x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer Answer: D Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

76) The landlord ran the model in Excel and received the answer report contained in the table. Which of the following statements is correct? Variable Cells Cell

Name

Original Value

Final Value

$G$4 $H$4 $G$5 $H$5 $G$6 $H$6 $G$7 $H$7

wood floors contractor wood floors self kitchen tile contractor kitchen tile self back door contractor back door self garage door opener contractor garage door opener self

1 1 1 1 1 1 1 1

0 1 1 0 0 0 0 0

A) The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900. B) The rent will be $195 higher and the project will take 2.5 weeks to finish at a cost of $2900. C) The rent will be $180 higher and the project will take 2.5 weeks to finish at a cost of $3700. D) The rent will be $195 higher and the project will take 3.5 weeks to finish at a cost of $3700. Answer: A Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

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77) The landlord ran the model in Excel and received the sensitivity report for the constraints as contained in the table. Which of the following statements is correct?

Cell

Name

$B$12 Total Time Weeks $E$10 Total Cost $I$4 wood floors Included? $I$5 kitchen tile Included? $I$6 back door Included? $I$7 garage door opener Included?

Final Value

Shadow Price

4.00 3000.00 1.00 1.00 0.00 1.00

13.64 0.01 67.27 25.45 0.00 11.82

Constraint Allowable Allowable

R.H. Side 4 3000 1 1 1 1

Increase 1.1 550 1.27E-16 7.63E-17 1.00E+30 5.09E-16

Decrease 3.1E-16 3.1E-13 4.6E-01 2.8E-01 1.0E+00 1.0E+00

A) If there are 2 more weeks available for work, it would be possible to increase rent by $27.28 per week B) Given the scenario, it is evident that a constraint is missing. C) If the landlord installed two garage doors, rent could be increased by $23.64. D) Given the scenario, it is evident that the objective function is misstated. Answer: B Diff: 3 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

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The Cruise Their cruise would port out of New Orleans and promised seven days with a panoply of excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site and key features of each appear in the table. The excursions were all day affairs, so it was possible to engage in only one per port. The cruise ship sailed at night and docked at each of these three ports at the crack of dawn. By dinner time, the ship was on its way to the next port and next set of excursions. The couple was energetic and active for a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't want to spend money on excursions that might be better spent on tacky souvenirs. The couple therefore budgeted $250 for the excursions — the prices shown are per couple, so for example, the $60 will pay for both of them to fill up on jerk chicken and mannish water. For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the couple researched the quality of the activity and ranked the excursion among the available alternatives, with higher numbers indicating better quality. Thus, snorkeling in Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3. Site Rating Activity Cost Jamaica 3 snorkeling $100 Jamaica 1 party island $95 Jamaica 2 horseback ride $120 Jamaica 3 local cuisine $60 Cozumel 2 snorkeling $110 Cozumel 3 party island $55 Cozumel 1 horseback ride $70 Cozumel 2 local cuisine $90 Cozumel 3 tequila tasting $130 Grand Cayman 1 snorkeling $90 Grand Cayman 2 party island $60 Grand Cayman 3 horseback ride $110 Grand Cayman 1 local cuisine $130 Grand Cayman 3 turtle farm $95 (Note - data used in this test question should not be construed as vacation advice.) 78) What is an appropriate objective function for this vacation? A) Max Z = JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu B) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu C) Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu D) Min Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu Answer: C Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

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79) Use the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) to represent the decision variables. What of these sets of constraints appropriately limits the number of excursions based on the scenario? A) JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3 B) JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1 C) JS + CS + GS ≤ 1 JP + CP + GP ≤ 1 JH + CH + GH ≤ 1 JL + CL + GL ≤ 1 D) JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu = 3 Answer: B Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

80) Use the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) to represent the decision variables. What of these alternative sets of constraints ensures that no activities are duplicated at the ports of call? A) JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3 B) JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1 C) JS + CS + GS ≤1 JP + CP + GP ≤1 JH + CH + GH ≤1 JL + CL + GL ≤1 D) JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu = 3 Answer: C Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

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81) In all the excitement of waving to the longshoremen as the ship leaves the Port of New Orleans, the management scientist drops his wallet in the Mississippi River. Rather than maximize enjoyment for the three excursions, he must now adjust his model to select three inexpensive options. Which combinations of objective function and constraints are best if the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) is used to represent the decision variables? A) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu subject to: JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1 B) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu subject to: JS + JP + JH + JL ≤ 1 CS + CP + CH + CL + CTe ≤ 1 GS + GP + GH + GL + GTu ≤ 1 C) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu JS + CS + GS ≤1 JP + CP + GP ≤1 JH + CH + GH ≤1 JL + CL + GL ≤1 D) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu = 3 Answer: A Diff: 2 Page Ref: 201-202 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming models, 0-1 integer programming models AACSB: Analytical thinking

82) Types of integer programming models are: A) total. B) 0-1. C) mixed. D) all of the above Answer: D Diff: 1 Page Ref: 186-188 Section Heading: Integer Programming Problems Keywords: integer programming models AACSB: Analytical thinking

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83) In a ________ integer model, some solution values for decision variables are integers and others can be non-integer. A) total B) 0-1 C) mixed D) all of the above Answer: C Diff: 2 Page Ref: 188 Section Heading: Integer Programming Problems Keywords: integer programming models, mixed integer models AACSB: Application of knowledge

84) In a ________ integer model, all decision variables have integer solution values. A) total B) 0-1 C) mixed D) all of the above Answer: A Diff: 2 Page Ref: 186 Section Heading: Integer Programming Problems Keywords: integer programming models AACSB: Application of knowledge

85) In a ________ integer model, the solution values of the decision variables are 0 or 1. A) total B) 0-1 C) mixed D) all of the above Answer: B Diff: 2 Page Ref: 184 Section Heading: Integer Programming Problems Keywords: integer programming models AACSB: Application of knowledge

86) Binary variables are: A) 0 or 1 only. B) any integer value. C) any continuous value. D) any negative integer value. Answer: A Diff: 1 Page Ref: 187 Section Heading: Computer Solution of Integer Program Probs w/Excel, QM for Win Keywords: integer programming formulation AACSB: Application of knowledge

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87) Which of the following is not an integer linear programming problem? A) pure integer B) mixed integer C) 0-1 integer D) continuous Answer: D Diff: 2 Page Ref: 186-188 Section Heading: Integer Programming Problems Keywords: integer programming models AACSB: Application of knowledge

88) If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: A) always optimal and feasible. B) sometimes optimal and feasible. C) always feasible. D) never optimal and feasible. Answer: B Diff: 3 Page Ref: 187 Section Heading: Integer Programming Graphical Solution Keywords: integer programming models AACSB: Analytical thinking

89) The branch and bound method of solving linear integer programming problems is: A) an integer method. B) a relaxation method. C) a graphical solution. D) an enumeration method. Answer: D Diff: 2 Page Ref: 191 Section Heading: Integer Programming Problems Keywords: integer programming solution methods, branch and bound method AACSB: Application of knowledge

90) If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem. A) always, optimal B) always, non-optimal C) never, non-optimal D) sometimes, optimal Answer: D Diff: 2 Page Ref: 190 Section Heading: Integer Programming Problems Keywords: integer programming solution, rounding off AACSB: Analytical thinking

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91) If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a feasible solution to the integer linear programming problem. A) always B) sometimes C) optimally D) never Answer: A Diff: 2 Page Ref: 190 Section Heading: Integer Programming Problems Keywords: integer programming solution, rounding off AACSB: Application of knowledge

92) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite Answer: B Diff: 2 Page Ref: 187 Section Heading: Integer Programming Problems Keywords: mutually exclusive constraints, 0-1 variables AACSB: Analytical thinking

34 .

Note Must get a cover if these are purchased Not needed unless we buy iPads Can't afford both this and the iPads Don't need if we have the electronic version Worthless without the iPads

93) Which constraint best describes the situation with decision variables A and B? A) B - A ≤ 0 B) B - A = 0 C) B + A = 1 D) B + A ≤ 1 Answer: B Diff: 2 Page Ref: 186-188 Section Heading: Integer Programming Models Keywords: 0-1 variables, multiple choice constraint AACSB: Analytical thinking

94) Which of the constraints best describes the relationship between the iPads for everyone and the speaker series? A) A - C ≤ 1 B) A + C = 1 C) A - C = 0 D) A + C = 2 Answer: B Diff: 2 Page Ref: 186-188 Section Heading: Integer Programming Models Keywords: 0-1 integer programming AACSB: Analytical thinking

35 .

95) Which of the following constraints best describes the relationship between the electronic Wall Street Journal subscription and the iPads? A) E - A = 0 B) E - A = 1 C) E - A ≤ 0 D) E - A ≤ 1 Answer: C Diff: 2 Page Ref: 186-188 Section Heading: Integer Programming Models Keywords: 0-1 variables, conditional constraints AACSB: Analytical thinking

96) Which of these formulations of the budget constraint is correct? Assume that there are 20 students in this semesters MBA class. A) $750A + $25B + $15,000C + $10D + $5E ≤ $56,250 B) 20A + 20B + C + 20D + 20E ≤ $56,250 C) A + B + C + D + E ≤ 20 D) $15,000A + $500B + $15,000C + $200D + $100E ≤ $56,250 Answer: D Diff: 2 Page Ref: 186-188 Section Heading: Integer Programming Models Keywords: integer linear programming formulation, capital budgeting AACSB: Analytical thinking

Saba conducts regular tours of his favorite city in the world, Paris. Each semester he selects among the finest students in the university and escorts them to the City of Lights. In addition to a world-class education on conducting business in Europe, he arranges a number of cultural outings for them to help them immerse themselves in all that France has to offer. He collects an extra $100 from each student for this purpose and limits his tour group to ten lucky individuals. Some of the events (and their prices) he proposes to the students include: Eiffel Tower visit, $40 per student, E Paris Sewer spelunking, $20 per student, S Half day passes to the Louvre, $60 per student, L Bon Beret tour, $50 per student, B So much to do and so little time! 97) Which constraint is most appropriate if the students can choose only three of these activities? A) E + S + L + B ≤ 3 B) $40E + $20S + $60L + $50B ≤ $100 C) E + S + L + B ≥ 2 D) E + S + L + B ≤ 4 Answer: A Diff: 2 Page Ref: 186-188 Section Heading: Integer Programming Models Keywords: 0-1 variables, multiple choice constraint AACSB: Analytical thinking

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98) If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite Answer: A Diff: 2 Page Ref: 188 Section Heading: Integer Programming Problems Keywords: multiple choice constraints, 0-1 variables AACSB: Application of knowledge

99) If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite Answer: C Diff: 2 Page Ref: 187 Section Heading: Integer Programming Problems Keywords: conditional constraints, 0-1 variables AACSB: Application of knowledge

100) If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite Answer: D Diff: 2 Page Ref: 187 Section Heading: Integer Programming Problems Keywords: corequisite constraints, 0-1 variables AACSB: Application of knowledge

101) For a maximization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the less-than-or-equal-to type. A) up and down B) up C) down D) up or down Answer: C Diff: 2 Page Ref: 190 Section Heading: Integer Programming Graphical Solution Keywords: integer linear programming solution AACSB: Analytical thinking

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102) In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? A) x1 + x2 + x5 ≤ 1 B) x1 + x2 + x5 ≥ 1 C) x1 + x5 ≤ 1, x2 + x5 ≤ 1 D) x1 - x5 ≤ 1, x2 - x5 ≤ 1 Answer: C Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming formulation, constraint AACSB: Analytical thinking

103) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, the constraint for the first restriction is : A) S1 + S3 + S7 ≥ 1. B) S1 + S3 + S7 ≤1. C) S1 + S3 + S7 = 2. D) S1 + S3 + S7 ≤ 2. Answer: D Diff: 3 Page Ref: 203 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, constraint AACSB: Analytical thinking

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DC 1 2 3

A 1 2 3

Region B C 3 3 4 1 2 2

D 2 3 3

The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. Assume that Xij = quantity shipped from distribution i to region j. i = 1,2,3 and j = 1, 2, 3, 4. Assume that Yi = 0 or 1 where i = distribution center 1, 2 or 3. 104) The constraint for distribution center 1 is: A) X11 + X12 + X13 + X14 - 500y1 ≤ 0. B) X11 + X12 + X13 + X14D + 500y1 ≤ 0. C) X11 + X12 + X13 + X14 ≤ 500. D) X11 + X12 + X13 + X14 ≥ 500. Answer: A Diff: 2 Page Ref: 184 Section Heading: Integer Programming Graphical Solution Keywords: facility location example, mixed integer programming AACSB: Analytical thinking

39 .

105) The objective function is A) Min Z =

B) Min Z =

C) Min Z =

D) Min Z =

Answer: A Diff: 3 Page Ref: 203 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: facility location example, mixed integer programming AACSB: Analytical thinking

106) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint(s) for the second restriction. A) S2 + S5 ≤ 1 B) S4 + S5 ≤ 1 C) S2 + S5 + S4 + S5 ≤ 2 D) S2 + S5 ≤ 1, S4 + S5 ≤ 1 Answer: D Diff: 3 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming formulation, constraint AACSB: Analytical thinking

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Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million. The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows: Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4. Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility)

107) The constraint for the North American supply region is: A) X11 + X21 + X31 + X34 - 5Y11 - 10Y21 ≤ 0. B) X11 + X12 + X13 + X14 - 5Y11 - 10Y12 ≤ 0. C) X11 + X12 + X13 + X14 - 3200Y11 - 4800Y12 ≤ 0. D) X11 + X12 + X13 + X14 - 5Y11 - 10Y12 = 0. Answer: B Diff: 3 Page Ref: 203 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: mixed integer linear programming problems AACSB: Analytical thinking

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108) The constraint for the South Asia demand region is: A) X31 + X32 + X33 + X34 =7. B) X31 + X32 + X33 + X34 ≤ 7. C) X13 + X23 + X33 + X43 ≤ 7. D) X13 + X23 + X33 + X43 = 7. Answer: D Diff: 3 Page Ref: 203 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: mixed integer linear programming problems AACSB: Analytical thinking

109) Which of these constraints will ensure that either a low capacity or a high facility capacity facility is built in the European supply region? A) Y41 + Y42 = 1 B) Y41 + Y42 ≤ 1 C) Y14 + Y24 = 1 D) Y14 + Y24 ≤ 1 Answer: A Diff: 3 Page Ref: 203 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: mixed integer linear programming problems AACSB: Analytical thinking

110) Which of these constraints will ensure that a low capacity facility is not built in South America? A) Y12 + Y22 ≤ 1 B) Y12 + Y22 = 1 C) Y12 + Y22 = 0 D) Y21 + Y22 ≤ 1 Answer: C Diff: 2 Page Ref: 203 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: mixed integer linear programming problems AACSB: Analytical thinking

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111) Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? A) x1 = 6, x2 = 4, Z = 54 B) x1 = 3, x2 = 6, Z = 51 C) x1 = 2, x2 = 6, Z = 46 D) x1 = 4, x2 = 6, Z = 56 Answer: D Diff: 2 Page Ref: 191-199 Section Heading: Computer Solution of Integer Program Probs w/Excel, QM for Win Keywords: integer programming solution AACSB: Analytical thinking

112) Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected. A) exactly 1, 2 B) exactly 2, 4 C) at least 2, 4 D) at most 1, 2 Answer: B Diff: 2 Page Ref: 201 Section Heading: 0-1 Integer Programming Modeling Examples Keywords: integer programming formulation, 0-1 integer programming AACSB: Analytical thinking

113) In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected. A) can also B) can sometimes C) can never D) must also Answer: D Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming formulation AACSB: Analytical thinking

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114) In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected. A) must always B) can sometimes C) can never D) is already Answer: B Diff: 2 Page Ref: 187 Section Heading: Integer Programming Models Keywords: integer programming formulation AACSB: Analytical thinking

115) In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 01 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is: A) 0. B) 1. C) 0 or 1. D) none of the above Answer: B Diff: 3 Page Ref: 187 Section Heading: Integer Programming Models Keywords: mixed integer programming problem AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 6 Transportation, Transshipment, and Assignment Problems 1) In a transportation problem, items are allocated from sources to destinations at a minimum cost. Answer: TRUE Diff: 1 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

2) In a transportation problem, items are allocated from sources to destinations at a maximum value. Answer: FALSE Diff: 1 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

3) The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination. Answer: TRUE Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Analytical thinking

4) In a balanced transportation model where supply equals demand, all constraints are equalities. Answer: TRUE Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: balanced transportation model AACSB: Analytical thinking

5) In an unbalanced transportation model, all constraints are equalities. Answer: FALSE Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: transportation problem, balanced transportation model AACSB: Analytical thinking

6) For most real-world applications, an unbalanced transportation model is a more likely occurrence than a balanced transportation model. Answer: TRUE Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: balanced transportation model AACSB: Application of knowledge

1 .

7) In order to model a "prohibited route" in a transportation or transshipment problem, the route should be omitted from the linear program. Answer: FALSE Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Analytical thinking

8) A prohibited route in a transportation model should be assigned a value of zero. Answer: FALSE Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: prohibited routes AACSB: Application of knowledge

9) A prohibited route in a transportation model should be assigned an arbitrarily high cost coefficient. Answer: TRUE Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: prohibited routes AACSB: Application of knowledge

10) In an unbalanced transportation problem, if demand exceeds supply, the optimal solution will be infeasible. Answer: FALSE Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

11) The transshipment model includes intermediate points between the sources and destinations. Answer: TRUE Diff: 3 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Application of knowledge

12) In a transshipment problem, items may be transported from sources through transshipment points on to destinations. Answer: TRUE Diff: 1 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Application of knowledge

13) In a transshipment problem, items may be transported from one source to another. Answer: TRUE Diff: 1 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Application of knowledge

2 .

14) In a transshipment problem, items may be transported from one transshipment point to another. Answer: TRUE Diff: 1 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Application of knowledge

15) In a transshipment problem, items may be transported from one destination to another. Answer: TRUE Diff: 1 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Application of knowledge

16) In a transshipment problem, items may be transported directly from sources to destinations. Answer: TRUE Diff: 1 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Application of knowledge

17) In a transshipment problem, items may be transported from destination to destination and from source to source. Answer: TRUE Diff: 1 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Application of knowledge

18) An assignment problem is a special form of transportation problem where all supply and demand values equal 1. Answer: TRUE Diff: 2 Page Ref: 251 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Application of knowledge

19) Assignment linear programs always result in integer solutions. Answer: TRUE Diff: 1 Page Ref: 251 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Application of knowledge

20) Networks may be used to represent assignment problems. Answer: TRUE Diff: 2 Page Ref: 254 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

3 .

21) In a transshipment model, the supply at each source and demand at each destination are limited to one unit. Answer: FALSE Diff: 1 Page Ref: 251 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Application of knowledge

22) In a ________ problem, items are allocated from sources to destinations at a minimum cost. Answer: transportation Diff: 1 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

23) In a ________ transportation model where supply equals demand, all constraints are equalities. Answer: balanced Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: balanced transportation model AACSB: Application of knowledge

24) In an unbalanced transportation problem, if supply exceeds demand, the shadow price for at least one of the supply constraints will be equal to ________. Answer: zero Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Analytical thinking

25) In order to model a "prohibited route" in a transportation or transshipment problem, the cost assigned to the route should be ________. Answer: high Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Analytical thinking

26) The ________ model is an extension of the transportation model in which intermediate points are added between the sources and destinations. Answer: transshipment Diff: 3 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Application of knowledge

4 .

27) An example of a ________ point is a distribution center or warehouse located between plants and stores. Answer: transshipment Diff: 2 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Application of knowledge

28) An appropriate choice of a model for analyzing the best shipping routes for a supply chain consisting of a manufacturer, warehouse, and retailer would be the ________ model. Answer: transshipment Diff: 2 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Application of knowledge

29) A form of the transportation problem in which all supply and demand values equal 1 is the ________ problem. Answer: assignment Diff: 2 Page Ref: 251 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Application of knowledge

30) A plant has four jobs to be assigned to four machines, and each machine has different manufacturing times for each product. The production manager wants to determine the optimal assignments of four jobs to four machines to minimize total manufacturing time. This problem can be most efficiently solved using the ________ model. Answer: assignment Diff: 2 Page Ref: 251 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

31) In a linear programming formulation of a transportation model, each of the possible combinations of supply and demand locations is a(n) ________. Answer: decision variable Diff: 2 Page Ref: 238 Section Heading: The Transportation Model Keywords: decision variables, model formulation AACSB: Analytical thinking

32) The cost to send a unit of product from supply source A to demand location B would be represented in the ________ of the linear programming statements. Answer: objective function Diff: 2 Page Ref: 238 Section Heading: The Transportation Model Keywords: objective function AACSB: Analytical thinking

5 .

33) In most real-world cases, the supply capacity and demanded amounts result in a(n) ________ transportation model. Answer: unbalanced Diff: 2 Page Ref: 240 Section Heading: The Transportation Model Keywords: unbalanced transportation problem AACSB: Application of knowledge

34) In order to prevent the accumulation of inventory at transshipment points, they should be modeled as being ________ nodes. Answer: balanced Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Analytical thinking

35) If the number of sources is greater than the number of destinations, then we have a(n) ________ assignment problem. Answer: unbalanced Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Application of knowledge

36) In an assignment problem, all demand and supply values are equal to ________. Answer: one Diff: 1 Page Ref: 251 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Application of knowledge

Consider the following transportation problem:

37) How many supply-side constraints are there? Write the supply-side constraints. Answer: 4 supply-side constraints + = 100 +

= 200

= 150

= 50

Diff: 2 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation prob, linear prog formulation of transportation prob AACSB: Analytical thinking

6 .

38) How many demand-side constraints are there? Write the demand-side constraints. Answer: 2 demand-side constraints x11 + x21 + x31 + x41 = 250 x12+ x22 + x32 + x42 = 250 Diff: 2 Page Ref: 238-239 Section Heading: The Transportation Model Keywords: transportation prob, linear prog formulation of transportation prob AACSB: Analytical thinking

39) If the optimal solution includes x11 = 100 and x22 = 200, determine the remaining shipments that will result in a minimum cost of $1700. Answer: x31 = 150, x42 = 50 Diff: 2 Page Ref: 238-239 Section Heading: The Transportation Model Keywords: transportation prob, computer solution of transportation prob AACSB: Analytical thinking

A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work, however their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does what manuscript. Estimates of editing times (in hours) for each manuscript by each editor is:

40) a) How many supply-side constraints are needed? b) How many demand-side constraints are needed? c) How many variables are involved in this assignment method? Answer: a) 5, b) 5, c) 25 Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assign prob, linear programming formulation of the assign prob AACSB: Analytical thinking

41) If the optimal assignments include manuscript 1 to editor B, manuscript 2 to editor E, and manuscript 3 to editor C with a total editing time of 47 minutes, what manuscripts are assigned to editors D and A? Answer: manuscript 4 to editor D and manuscript 5 to editor A Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assign prob, linear programming formulation of the assign prob AACSB: Analytical thinking

7 .

42) What are the linear programming constraints for manuscript 1 and editor C? Answer: x1A + x1B + x1C + x1D+ x1E = 1 x1C + x2C + x3C + x4C+ x5C = 1 Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: linear programming formulation AACSB: Analytical thinking

43) Write the assignment problem matrix below as a network flow problem. Assume that the numbers in each cell represent the travel distance required between nodes. The dash indicates that there is not a route between nodes.

1 2 3

A 4 3

B 6 2 5

C 1 9

Answer:

Diff: 2 Page Ref: 252 Section Heading: Computer Solution of the Assignment Problem Keywords: assignment problem, network AACSB: Analytical thinking

8 .

Awards committees need to be formed to review potential award recipients. In the past, three people have been assigned to review each applicant. The only stipulation is that a reviewer cannot be assigned to an applicant if the applicant is a co-worker. The matrix below shows 9 reviewers, 3 candidates, and a matrix. If an entry in the matrix contains an "X", then that specific reviewer is ineligible to review an applicant's material. For example, reviewer 1 cannot review materials submitted by candidate B. It is possible that some reviewers may not receive an assignment.

Reviewer 1 2 3 4 5 6 7 8 9

Applicant A B X X

X X X X X X

44) Formulate this as an assignment problem in which two reviewers are assigned to review each applicant's material. Answer: X1A + X1B + X1C ≤ 1 X2A + X2B + X2C ≤ 1 X3A + X3B + X3C ≤ 1 X4A + X4B + X4C ≤ 1 X5A + X5B + X5C ≤ 1 X6A + X6B + X6C ≤ 1 X7A + X7B + X7C ≤ 1 X8A + X8B + X8C ≤ 1 X9A + X9B + X9C ≤ 1 X1A + X3A + X4A + X6A + X7A + X8A + X9A = 2 X2B + X3B + X4B + X5B + X8B = 2 X1C + X2C + X4C + X5C + X6C + X7C + X9C = 2 Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

9 .

45) A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign two reviewers to Applicant B and 1 additional reviewer to Applicant C.

Reviewer 1 2 3 4 5 6 7 8 9 Demand Assigned

Applicant B X

C 1 X

1 X X X 1 2 2

X X 2

Answer: This is one possible solution. Another is to assign reviewer 9 to applicant C.

Reviewer 1 2 3 4 5 6 7 8 9 Demand Assigned

A 0 0 0 1 0 0 0 1 0 2 2

Applicant B 0 0 1 0 1 0 0 0 0 2 2

C 1 1 0 0 0 0 0 0 0 2 2

Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

10 .

46) The committee would like to assign three reviewers to each applicant. A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign reviewers to Applicant B and Applicant C.

Reviewer 1 2 3 4 5 6 7 8 9

Applicant A B X X 1 1 X X X

X 1

Answer: Multiple optimal solutions

Reviewer 1 2 3 4 5 6 7 8 9 Assigned

A 0 0 1 1 0 0 0 0 1 3

Applicant B 0 1 0 0 1 0 0 1 0 3

C 1 0 0 0 0 1 1 0 0 3

A 1 0 1 0 0 1 0 0 0 3

Applicant B 0 1 0 0 1 0 0 1 0 3

C 0 0 0 1 0 0 1 0 1 3

Diff: 2 Page Ref: 252 Section Heading: Computer Solution of the Assignment Problem Keywords: assignment problem AACSB: Analytical thinking

11 .

In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodes and between all intermediate nodes and all destinations for a given transshipment problem. In addition, assume that no travel is possible between source nodes, between intermediate nodes, and between destination nodes, and no direct travel from source nodes to destination nodes. Let the source nodes be labeled as 1, 2, 3, the intermediate nodes be labeled as 4 and 5, and the destination nodes be labeled as 6 and 7. 47) State the constraint for intermediate node 4. Answer: X14 + X24 + X34 - X46 - X47 = 0 Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transship prob, linear prog formulation of transshipment prob AACSB: Analytical thinking

48) If there are 300 units available at source 2, state the constraint for source node 2. Answer: X24 + X25 = 300 Diff: 1 Page Ref: 248 Section Heading: The Transportation Model Keywords: transship prob, linear prog formulation of transshipment prob AACSB: Analytical thinking

49) If there are 175 units demanded at destination 6, state the constraint for destination 6. Answer: X46 + X56 = 175 Diff: 1 Page Ref: 248 Section Heading: The Transportation Model Keywords: transship prob, linear prog formulation of transshipment prob AACSB: Analytical thinking

12 .

Madlantic Devices designs and manufactures high-end medical devices. The facilities in Madison and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Dayton, Bloomington, or Albany. Manufacturing capacity in Madison and Atlanta is 1000 units. Demand at Dayton, Bloomington, and Albany is 450, 500, and 610, respectively. The network representing the shipping routs is shown below.

The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted.

50) What is the objective function for this problem? Use the notation Xij, where i and j correspond to the node numbers indicated in the diagram. Answer: MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47 Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

13 .

51) What is the constraint for the transshipment node in Knoxville? Answer: X14 + X24 + X34 - X43 - X45 - X46 - X47 = 0 Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

52) What is the constraint for Bloomington? Answer: X36 + X46 = 500 Diff: 1 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

Mondo's Runway Show Mondo Guerra is matching his models with his latest collection for Fashion Week. He has five models, ranging from 5'10" to 5'10.5" and size 0 to size 1. His five latest designs run the gamut from prêt-à-porter to an evening gown and he'd like to make sure each outfit looks as good as possible by having it worn on the runway by the right model. After an anxious month of sewing, he has each model try on each outfit and he assigns a fabulosity score to each combination as indicated in the table.

Zoe Yvette Xena Whisper Vajay

Gown 9 3 4 1 4

Sport 9 8 7 6 9

Couture 4 3 3 5 9

Avant Garde 4 8 7 6 6

Prêt-à-Porter 2 9 8 9 7

53) What is an appropriate objective function for this scenario? Answer: Using a Model-Outfit sequence for the decision variables yields the following: Max Fabulosity = 9ZG + 9ZS + 4ZC + 4ZZA + 2ZP + 3YG + 8YS + 3YC + 8YA + 9YP + 4XG + 7XS + 3XC + 7XA + 8XP + 1WG + 6WS + 5WC + 6WA + 9WP + 4VG + 9VS + 9VC +6VA + 7VP Diff: 1 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment model formulation AACSB: Analytical thinking

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54) How many constraints does this model have? Provide a description in English for each one, without writing it mathematically. Answer: The model has r + c or 10 constraints, not counting the nonnegativity constraint. The row constraints could be summarized as "Each model must wear one outfit," and the column constraints can be summarized as "Each outfit must be worn by a model." Individually, the constraints would be articulated as: Zoe must wear one outfit. Yvette must wear one outfit. Xena must wear one outfit. Whisper must wear one outfit. Vajay must wear one outfit. The gown must be worn. The sport outfit must be worn. The couture must be worn. The avant garde must be worn. The prêt-à-porter outfit must be worn. Diff: 1 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment model formulation, constraints AACSB: Analytical thinking

55) Help Mondo make the best choice of outfit for each model using linear programming. Answer: Using a Model-Outfit sequence for the decision variables yields the following: Max Fabulosity = 9ZG + 9ZS + 4ZC + 4ZA + 2ZP + 3YG + 8YS + 3YC + 8YA + 9YP + 4XG + 7XS + 3XC + 7XA + 8XP + 1WG + 6WS + 5WC + 6WA + 9WP + 4VG + 9VS + 9VC +6VA + 7VP Subject to: ZG + ZS + ZC + ZA + ZP = 1 YG + YS + YC + YA + YP = 1 XG + XS + XC + XA + XP =1 WG + WS + WC + WA + WP = 1 VG + VS + VC + VA + VP = 1 ZG + YG + XG + WG + VG = 1 ZS + YS + XS +WS +VS = 1 ZC + YC + XC + WC + VC = 1 ZA + YA + XA + WA + VA = 1 ZP + YP + XP + WP + VP = 1 ZG, ZS, ZC, ZA, ZP, YG, YS, YC, YA, YP, XG, XS, XC, XA, XP, WG, WS, WC, WA, WP, VG, VS, VC, VA, VP ≥ 0 Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment model formulation, constraints AACSB: Analytical thinking

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56) Mondo has never heard of linear programming and you don't have your laptop handy. Provide him with a "best case" total fabulosity number Answer: The greatest possible value is 45, since there are 5 scores that will be chosen and the scores range from 1 to 9. Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

57) You formulate this as an assignment model and review the Zoe section of the sensitivity analysis with Mondo. Provide him with an interpretation.

Cell

Name

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease

$J$13 Zoe Gown $K$13 Zoe Sport $L$13 Zoe Leisure $M$13 Zoe Cocktail $N$13 Zoe Pret a Porter

1 0 0 0 0

0 0 -2 -5 -8

9 9 4 4 2

1E+30 3 2 5 8

3 2 1E+30 1E+30 1E+30

Answer: Zoe is assigned to wear the gown and will add 9 points to the overall fabulosity score. Even if Zoe's rating in the gown was up to 3 points lower, she would still be assigned to wear the gown. The overall score would be lower, but this would still be her assignment. Normally, the reduced cost entries speak to the change in objective coefficients before the assignment changes. As the model was presented, the coefficient for Zoe in the Leisure outfit was 4, with a reduced cost of -2, so a change in excess of 4 to 4-2 = 6 would cause the Leisure outfit assignment to be optimal. As this is a balanced model, we cannot make that statement. Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

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58) Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region.

DC 1 2 3

A 1 2 3

Region B C 3 3 4 1 2 2

D 2 3 3

The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. Define the decision variables for this situation. Answer: y1 = 1 if DC1 is selected, 0 otherwise y2 = 1 if DC2 is selected, 0 otherwise y3 = 1 if DC3 is selected, 0 otherwise x1A = quantity shipped from DC 1 to Region A x1B = quantity shipped from DC 1 to Region B x1C = quantity shipped from DC 1 to Region C x1D = quantity shipped from DC 1 to Region D x2A = quantity shipped from DC 2 to Region A x2B = quantity shipped from DC 2 to Region B x2C = quantity shipped from DC 2 to Region C x2D = quantity shipped from DC 2 to Region D x3A = quantity shipped from DC 3 to Region A x3B = quantity shipped from DC 3 to Region B x3C = quantity shipped from DC 3 to Region C x3D = quantity shipped from DC 3 to Region D Diff: 2 Page Ref: 238-240 Section Heading: The Transportation Model Keywords: facility location example, mixed integer programming AACSB: Analytical thinking

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59) Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region.

DC 1 2 3

A 1 2 3

Region B C 3 3 4 1 2 2

D 2 3 3

The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. Write the objective function for this problem. Answer: Min Z = 1x1A + 3x1B + 3x1C + 2x1D + 2x2A + 4x2B + 1x2C + 3x2D + 3x3A + 2x3B + 2x3C +3x3D + 500y1 + 600y2 + 525y3 Diff: 2 Page Ref: 238-240 Section Heading: The Transportation Model Keywords: facility location example, mixed integer programming AACSB: Analytical thinking

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60) Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region.

DC 1 2 3

A 1 2 3

Region B C 3 3 4 1 2 2

D 2 3 3

The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. Write the constraints for the 3 distribution centers. Answer: x1A + x1B +x1c - 500y1 ≤ 0 x2A + x2B +x2c - 500y2 ≤ 0 x3A + x3B +x3c - 500y3 ≤ 0 Diff: 2 Page Ref: 238-240 Section Heading: The Transportation Model Keywords: facility location example, mixed integer programming AACSB: Analytical thinking

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Semester Prep The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below.

Saba Geoff Tim David

Intro to Ops 3 4 5 4

Project Mgt 10 19 11 11

Quality Mgt 12 2 4 4

Control 16 10 14 15

Logistics 12 8 14 17

Mgt Science 7 18 3 15

61) What is an appropriate objective function for this scenario? Answer: Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops: Min Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: transportation model AACSB: Analytical thinking

62) Write the model that is suitable for this scenario. Answer: Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops: Min Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM SI + SP + SQ + SC + SL + SM ≤ 3 SI + SP + SQ + SC + SL + SM ≥ 2 GI + GP + GQ + GC + GL + GM ≤ 3 GI + GP + GQ + GC + GL + GM ≥ 2 TI + TP + TQ + TC + TL + TM ≤ 3 TI + TP + TQ + TC + TL + TM ≥ 2 DI + DP + DQ + DC + DL + DM ≤ 3 DI + DP + DQ + DC + DL + DM ≥ 2 SI + GI + TI + DI ≥ 6 SP + GP + TP + DP = 1 SQ + GQ + TQ+ DQ = 1 SC + GC + TC + DC = 1 SL + GL + TL+ DL = 1 SM + GM + TM + DM = 1 Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: transportation model AACSB: Analytical thinking

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63) Take note of the phrase in the scenario that reads "Naturally, every professor in the department had his own pet course..." Provide an example of a constraint that makes sure a professor gets to teach his favorite course. Answer: Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, we can ensure that Saba is assigned to Intro to Operations by entering the constraint: SI ≥ 2 along with the other constraints in the model. If Geoff likes Logistics, then GL = 1 would assign that professor the logistics class. Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: transportation model AACSB: Analytical thinking

64) The department chair is eager to motivate the senior faculty to consider retirement and wants to burden them as much as possible. What should the model look like that otherwise meets departmental objectives? Answer: Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, Max Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM SI + SP + SQ + SC + SL + SM = 3 GI + GP + GQ + GC + GL + GM = 3 TI + TP + TQ + TC + TL + TM = 3 DI + DP + DQ + DC + DL + DM = 3 SI + GI + TI + DI ≥ 6 SP + GP + TP + DP = 1 SQ + GQ + TQ+ DQ = 1 SC + GC + TC + DC = 1 SL + GL + TL+ DL = 1 SM + GM + TM + DM = 1 The difference between this model and the benevolent chair model is that this is formulated to maximize prep time and assigns each professor a three-course load. The benevolent chair model minimizes prep time and allows for a two-course teaching load. Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: transportation model AACSB: Analytical thinking

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65) The department chair looks at past course evaluations and realizes that if she wants to attract students to the Operations and Supply Chain major, it would be best if Geoff were never assigned to teach that class. How can her standard model be modified to ensure that Geoff cannot scare away students from the major? Answer: Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, these additions should be made to the base model. SI + TI + DI ≥ 6 GI = 0 The difference between this model and the base is that this assigns Geoff to no sections of Introduction to Operations, while maintaining he number of sections at six or greater among the other three faculty members. This model's objective is still to minimize the number of prep hours. As luck would have it, this model performs as well as the base model, which didn't have any sections of Intro assigned to Geoff. Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: transportation model AACSB: Analytical thinking

66) What special case of linear programming should be used to model this situation? Answer: The scenario gives the appearance that it is an assignment model waiting to happen up until the point that six sections of Introduction to Operations are needed and the professors are responsible for two to three sections each. The easiest way to model this is by declaring it a transportation model with the six sections of Introduction to Operations as traveling to the same destination. However, if each of those six sections is a node unto itself, and if each professor is separated into three possible sources of teaching, then this would fit the assignment model. The problem with solving the scenario with an assignment model is that the number of decision variables increases from 24 to 132 and the constraints increase from 10 to 23. Diff: 3 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation model AACSB: Application of knowledge

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. 67) Write every constraint that involves Company A. Answer: A's supply constraint is AD + AE = 200 D's balance constraint is AD + BD + CD - DF - DG - DH = 0 E's balance constraint is AE + BE + CE - EF - EG - EH = 0 Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

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68) What is the complete linear model for this scenario? Answer: Min Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH AD + AE = 200 BD + BE = 300 CD + CE = 500 DF + EF = 350 DG + EG = 450 EF + EH = 200 AD + BD + CD - DF - DG - DH = 0 AE + BE + CE - EF - EG - EH = 0 AD + BD + CD ≤ 600 AE + BE + CE ≤ 700 Diff: 3 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

69) What are the objective function terms that involve the demand locations? Answer: $4DF + $4DG + $4DH + $10EF + $9EG + $8EH Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

70) How would the transshipment location constraints read if it was OK to store product there on a temporary basis? Answer: AD + BD + CD - DF - DG - DH ≥ 0 AE + BE + CE - EF - EG - EH ≥ 0 Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment AACSB: Analytical thinking

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71) Sketch the network for this problem and label all nodes and arrows with the appropriate information. Answer:

Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

72) In a balanced transportation model where supply equals demand: A) all constraints are equalities. B) none of the constraints are equalities. C) all constraints are inequalities. D) none of the constraints are inequalities. Answer: A Diff: 3 Page Ref: 240 Section Heading: The Transportation Model Keywords: balanced transportation model AACSB: Analytical thinking

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Zoe Yvette Xena Whisper Vajay

Gown 9 3 4 1 4

Sport 9 8 7 6 9

Couture 4 3 3 5 9

Avant Garde 4 8 7 6 6

73) What is an appropriate constraint for this scenario? A) ZG + ZS + ZC + ZA + ZP = 1 B) ZG + ZS + ZC + ZA + ZP ≤ 1 C) 9ZG + 9ZS + 4ZC + 4ZA +2 ZP ≥ 1 D) 9ZG + 9ZS + 4ZC + 4ZA +2 ZP = 1 Answer: A Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment model formulation AACSB: Analytical thinking

74) What is an appropriate constraint for this scenario? A) ZG + YG + XG + WG + VG ≤ 1 B) ZG + YG + XG + WG + VG = 1 C) 9ZG + 3YG + 4XG + 1WG + 4VG ≥ 1 D) 9ZG + 3YG + 4XG + 1WG + 4VG = 1 Answer: A Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment model formulation AACSB: Analytical thinking

75) Which term does not belong in an objective function for this scenario? A) 9WP B) 4XG C) 6XC D) 9ZG Answer: C Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment model formulation AACSB: Analytical thinking

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Prêt-à-Porter 2 9 8 9 7

76) What is the best overall fabulosity score that Mondo can hope for? A) 9 B) 25 C) 36 D) 45 Answer: D Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment model formulation AACSB: Analytical thinking

77) Mondo ran the problem in Excel and has copied a portion of the sensitivity report below.

Cell

Name

$J$13 Zoe Gown $K$13 Zoe Sport $L$13 Zoe Leisure $M$13 Zoe Cocktail $N$13 Zoe Pret a Porter

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 1 0 0 0 0

0 0 -2 -5 -8

9 9 4 4 2

1E+30 3 2 5 8

3 2 1E+30 1E+30 1E+30

What is a reasonable conclusion that can be drawn from this section of the report? A) Zoe will contribute 9 points to the overall fabulosity score of the model. B) It doesn't matter whether Zoe wears the sport outfit or the gown. C) The sport outfit has a range of 5 in fabulosity. D) Wearing the cocktail dress would lower the overall fabulosity score by 5 points. Answer: A Diff: 2 Page Ref: 252 Section Heading: Computer Solution of the Assignment Problem Keywords: assignment model formulation AACSB: Analytical thinking

78) Mondo ran the problem in Excel but used "≤ 1" constraints everywhere instead of "= 1" constraints. The objective function is formulated correctly and the general structure of the constraints is also correct, except for the inequality. What is a reasonable conclusion that can be drawn from this formulation of the model? A) None of the outfits will be worn. B) There would be no difference in the model results from one with = constraints. C) A model may be assigned two different outfits. D) An outfit may be assigned to two different models. Answer: B Diff: 2 Page Ref: 252 Section Heading: Computer Solution of the Assignment Problem Keywords: assignment model formulation AACSB: Analytical thinking

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79) Mondo ran the problem in Excel but wondered what would happen if he allowed his favorite model Xena to wear two outfits. She would be the first to walk the runway, then would change and also be the last model in the show. The sensitivity analysis for the original problem scenario is shown below.

Cell

Name

$J$20 Gown $K$20 Sport $L$20 Leisure $M$20 Cocktail $N$20 Pret_a_Porter $P$13 Zoe_wears $P$14 Yvette_wears $P$15 Xena_wears $P$16 Whisper_wears $P$17 Vajay_wears

Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 1 1 1 1 1 1 1 1 1 1

8 8 5 8 9 1 0 -1 0 4

1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 1 1 1 0 0

1 1 0 1 1 0 0 0 1E+30 0

What would happen if Mondo ran the model again, but this time changed the existing constraints to ≤ constraints and included a constraint that required Xena to model two separate looks? A) Xena would wear the pret-a-porter and the gown. B) Xena would wear the pret-a-porter and the cocktail. C) The overall fabulosity score would drop by 1. D) Xena would keep the same outfit. Answer: C Diff: 2 Page Ref: 252 Section Heading: Computer Solution of the Assignment Problem Keywords: assignment model formulation AACSB: Analytical thinking

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Saba Geoff Tim David

Intro to Ops 3 4 5 4

Project Mgt 10 19 11 11

Quality Mgt 12 2 4 4

Control 16 10 14 15

Logistics 12 8 14 17

Mgt Science 7 18 3 15

80) What is an appropriate objective function for this scenario? A) Max Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM B) Min Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM C) Min Z = SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM + TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM D) Max Z = SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM + TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM Answer: B Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: assignment model formulation AACSB: Analytical thinking

81) Which constraint is appropriate for this scenario? A) DI + DP + DQ + DC + DL + DM = 2 B) SI + GI + TI + DI ≤ 6 C) SM + GM + TM + DM ≥ 1 D) SI + SP + SQ + SC + SL + SM ≤ 3 Answer: D Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: assignment model formulation AACSB: Analytical thinking

28 .

82) Which constraint ensures that Introduction to Operations is offered according to the scenario? A) SI + GI + TI + DI ≥ 6 B) SI + GI + TI + DI ≤ 6 C) SI + SP + SQ + SC + SL + SM ≤ 6 D) SI + SP + SQ + SC + SL + SM ≥ 6 Answer: A Diff: 1 Page Ref: 239 Section Heading: The Transportation Model Keywords: assignment model formulation AACSB: Analytical thinking

83) David is qualified to teach Management Science, but has misplaced his slide rule and doesn't feel he can complete the necessary calculations if he is assigned to teach it next semester. Which of these constraints would ensure that he isn't the instructor? A) DI + DP + DQ + DC + DL ≥ 2 B) SM + GM + TM + DM ≤ 1 C) DM = 0 D) DI + DP + DQ + DC + DL + DM ≤ 3 Answer: C Diff: 1 Page Ref: 239 Section Heading: The Transportation Model Keywords: assignment model formulation AACSB: Analytical thinking

84) Copied below is a portion of the answer report that shows the constraints related to the faculty assignment. Which of these statements is best according to the answer report? Cell

Name

Cell Value

$S$15 $S$15 $S$16 $S$16 $S$17 $S$17 $S$18

Saba_assigned Saba_assigned Geoff_assigned Geoff_assigned Tim_assigned Tim_assigned David_assigned

3 3 3 3 2 2 3

Formula

Status

$S$15<=$Q$15 Binding $S$15>=$T$15 Not Binding $S$16<=$Q$16 Binding $S$16>=$T$16 Not Binding $S$17<=$Q$17 Not Binding $S$17>=$T$17 Binding $S$18<=$Q$18 Binding

A) Geoff is assigned to teach Introduction to Operations. B) Tim is assigned to teach two courses. C) David is assigned to teach Management Science. D) Saba is assigned to teach two courses. Answer: B Diff: 1 Page Ref: 239 Section Heading: The Transportation Model Keywords: assignment model formulation AACSB: Analytical thinking

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Slack 0 1 0 1 1 0 0

85) Copied below is a portion of the answer report that shows the status of the variable cells related to the faculty assignment. Which of these statements is consistent with the answer report? Cell

Name

$J$15 Saba Intro $K$15 Saba Project Mgt $L$15 Saba Quality Control $M$15 Saba Planning/Control $N$15 Saba Logistics $O$15 Saba Mgt Science $J$16 Geoff Intro

Original Value

Final Value

Integer

1 1 1 1 1 1 1

2 0 0 0 0 1 0

Contin Contin Contin Contin Contin Contin Contin

A) Geoff is assigned to teach Introduction to Operations. B) Tim is assigned to teach two courses. C) David is assigned to teach Introduction to Operations D) Saba is assigned to teach two courses. Answer: C Diff: 3 Page Ref: 239 Section Heading: The Transportation Model Keywords: assignment model formulation AACSB: Analytical thinking

86) In a transportation problem, items are allocated from sources to destinations: A) at a maximum cost. B) at a minimum cost. C) at a minimum profit. D) at a minimum revenue. Answer: B Diff: 1 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

87) The linear programming model for a transportation problem has constraints for supply at each ________ and ________ at each destination. A) destination, source B) source, destination C) demand, source D) source, demand Answer: D Diff: 1 Page Ref: 238 Section Heading: The Transportation Model Keywords: linear programming model for a transportation problem AACSB: Application of knowledge

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88) Which of the following assumptions is not an assumption of the transportation model? A) Shipping costs per unit are constant. B) There is one transportation route between each source and destination. C) There is one transportation mode between each source and destination. D) Actual total supply and actual total demand must be equal. Answer: D Diff: 2 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation model AACSB: Analytical thinking

89) The problem that deals with the distribution of goods from several sources to several destinations is the: A) network problem. B) assignment problem. C) transportation problem . D) transshipment problem. Answer: C Diff: 1 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

90) In the linear programming formulation of a transportation network: A) there is one variable for each arc. B) there is one constraint for each node. C) the sum of variables corresponding to arcs out of an source node is constrained by the supply at that node. D) all of the above Answer: D Diff: 2 Page Ref: 238 Section Heading: The Transportation Model Keywords: linear programming formulation of a transportation problem AACSB: Analytical thinking

91) The assignment problem constraint x41 + x42 + x43 + x44 ≤ 3 means: A) agent 3 can be assigned to 4 tasks. B) agent 4 can be assigned to 3 tasks. C) a mixture of agents 1, 2, 3 and 4 will be assigned to tasks 1, 2 or 3. D) There is no feasible solution. Answer: B Diff: 3 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

31 .

92) Which of the following are assumptions or requirements of the transportation problem? A) There must be multiple sources. B) Goods are the same, regardless of source. C) There must be multiple destinations. D) There must be multiple routes between each source and each destination. Answer: B Diff: 2 Page Ref: 238 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.

93) The constraint that represents the quantity supplied by DC 1 is: A) 4X1A + 6X1B + 8X1C ≤ 500. B) 4X1A + 6X1B + 8X1C = 500. C) X1A + X1B + X1C ≤ 500. D) X1A + X1B + X1C = 500. Answer: C Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: transportation problem, supply constraint AACSB: Analytical thinking

94) The constraint that represents the quantity demanded by Customer B is: A) 6X1B + 2X2B + 8X3B ≤ 350. B) 6X1B + 2X2B + 8X3B = 350. C) X1B + X2B + X3B ≤ 350. D) X1B + X2B + X3B = 350. Answer: D Diff: 2 Page Ref: 239 Section Heading: The Transportation Model Keywords: transportation problem, demand constraint AACSB: Analytical thinking

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95) In a transshipment problem, items may be transported: A) from destination to destination. B) from one transshipment point to another. C) directly from sources to destinations. D) all of the above Answer: D Diff: 2 Page Ref: 246 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Application of knowledge

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2.

Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. 96) Which constraint represents transshipment through the distribution center? A) 2X13 + 3X23 = 900 B) 2X13 + 3X23 + 5X34 + 4X35 + 3X36 = 0 C) X13 + X23 - X34 - X35 - X36 = 0 D) X13 + X23 - X34 - X35 - X36 ≥ 0 Answer: C Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment AACSB: Analytical thinking

33 .

97) Which constraint represents the quantity shipped to retail outlet 6? A) X23 + X36 = 450 B) X23 + X36 + X26 = 450 C) X36 + X26 ≤ 450 D) X36 + X26 = 450 E) 3X36 + 5X26 = 450 Answer: D Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment AACSB: Analytical thinking

98) In an assignment problem all supply and demand values equal are: A) 0. B) 1. C) 2. D) greater than 1. Answer: B Diff: 2 Page Ref: 247 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

99) In the process of evaluating location alternatives, the transportation model method minimizes the: A) total demand. B) total supply. C) total shipping cost. D) number of destinations. Answer: C Diff: 1 Page Ref: 238 Section Heading: The Assignment Model Keywords: transportation model AACSB: Application of knowledge

100) The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means: A) agent 3 can be assigned to 2 tasks. B) agent 3 can be assigned to no more than 2 tasks. C) a mixture of agents 1, 2, 3 and 4 will be assigned to tasks. D) agents 1, 2, 3, and 4 can be assigned up to 2 tasks. Answer: B Diff: 3 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment problem AACSB: Analytical thinking

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101) In an assignment problem: A) one agent can do parts of several tasks. B) one task can be done by only one agent. C) each agent is assigned to its own best task. D) several agents can do parts of one task. Answer: B Diff: 1 Page Ref: 251 Section Heading: Computer Solution of the Assignment Problem Keywords: assignment problem AACSB: Analytical thinking

102) The difference between the assignment and the transportation problem is that: A) total supply must equal total demand in the assignment problem. B) the number of origins must equal the number of destinations in the transportation problem. C) each supply and demand value is 1 in the assignment problem. D) both A and B Answer: C Diff: 2 Page Ref: 251 Section Heading: Computer Solution of the Assignment Problem Keywords: assignment and the transportation problems AACSB: Analytical thinking

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The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted.

103) The transshipment locations are: A) Madison and Atlanta. B) Philadelphia and Knoxville. C) Madison, Atlanta, Philadelphia and Knoxville. D) Dayton, Bloomington, and Albany. Answer: B Diff: 1 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment AACSB: Application of knowledge

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104) The constraint for the quantity shipped from Madison is: A) X13 + X 14 = 1000. B) X13 + X 14 ≤ 1000. C) X13 + X 14 ≥ 1000. D) X13 + X 14 - X34 = 1000. Answer: B Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment AACSB: Analytical thinking

105) The constraint for Philadelphia is: A) X13 + X23 - X35 - X36 - X37 = 0. B) X13 + X23 - X35 - X36 - X37 ≥ 0. C) X13 + X23 + X43 - X34 - X35 - X36 - X37 = 0. D) X13 + X23 + X43 - X34 - X35 - X36 - X37 ≥ 0. Answer: C Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

106) The objective function is: A) MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47. B) MIN 7X13 + 8X14 + 4X23 + 7X24 - 3X34 - 3X43 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47. C) MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 - 25X35 - 6X36 - 17X37 - 29X45 - 8X46 - 5X47. D) MIN 7X13 + 8X14 + 4X23 + 7X24 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47. Answer: A Diff: 2 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment AACSB: Analytical thinking

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A professor needs help from three student helpers to complete four tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below.

107) How many tasks will be assigned to the students? A) 2 tasks B) 3 tasks C) 4 tasks D) none, because the students take too long Answer: B Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment AACSB: Analytical thinking

108) Which of the following constraints represents the assignment for student A? A) XA1 + XA2 + XA3 + XA4 = 0 B) XA1 + XA2 + XA3 + XA4 = 1 C) XA1 + XA2 + XA3 + XA4 ≤ 1 D) XA1 + XA2 + XA3 + XA4 ≥ 0 Answer: B Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment AACSB: Analytical thinking

109) Which of the following constraints represents the assignment for task 2, scanning? A) X2A + X2B + X2C = 0 B) X2A + X2B + X2C = 1 C) X2A + X2B + X2C ≤ 1 D) X2A + X2B + X2C ≥ 0 Answer: C Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment AACSB: Analytical thinking

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110) Based on the information in the table, which tasks are least likely to be assigned to a student? A) grading B) scanning C) copying D) organizing portfolios Answer: A Diff: 2 Page Ref: 252 Section Heading: The Assignment Model Keywords: assignment AACSB: Analytical thinking

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. 111) Which of these constraints allows for some inventory to be held at one of the crossdock facilities? A) AD + BD + CD - DF - DG - DH ≥ 0 B) AD + BD + CD - DF - DG - DH = 600 C) AD + BD + CD = DF - DG - DH = 600 D) AD + BD + CD + DF + DG + DH = 600 Answer: A Diff: 1 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment AACSB: Analytical thinking

112) Which of these is not an element of the objective function? A) 4DF B) 600D C) 9EG D) 3CE Answer: B Diff: 1 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment problem AACSB: Analytical thinking

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113) How many decision variables are in this problem? A) 8 B) 9 C) 10 D) 12 Answer: D Diff: 1 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment AACSB: Analytical thinking

114) How many constraints are required to model this as a linear program? A) 8 B) 9 C) 10 D) 12 Answer: C Diff: 1 Page Ref: 248 Section Heading: The Transportation Model Keywords: transshipment model AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 7 Network Flow Models 1) A network is an arrangement of paths connected at various points through which items move. Answer: TRUE Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow models AACSB: Application of knowledge

2) Nodes represent junction points connecting branches. Answer: TRUE Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow models, nodes AACSB: Application of knowledge

3) Branches connect nodes and show flow from one point to another. Answer: TRUE Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow models, branches AACSB: Application of knowledge

4) The values assigned to branches typically represent distance, time, or cost. Answer: TRUE Diff: 1 Page Ref: 297 Section Heading: Network Components Keywords: network flow models, branches AACSB: Application of knowledge

5) Flows in a network can only be in one direction. Answer: FALSE Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow models AACSB: Application of knowledge

6) The shortest route problem is to find the shortest distance between an origin and various destination points. Answer: TRUE Diff: 1 Page Ref: 297 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Application of knowledge

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7) Once the shortest route to a particular node has been determined, that node becomes part of the permanent set. Answer: TRUE Diff: 1 Page Ref: 298 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Application of knowledge

8) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the minimal spanning tree. Answer: FALSE Diff: 1 Page Ref: 297 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

9) The shortest route network problem could help identify the best route for pizza delivery drivers from the pizza parlor to a specific customer. Answer: TRUE Diff: 2 Page Ref: 297 Section Heading: The Shortest Route Problem Keywords: network flow models, shortest route AACSB: Analytical thinking

10) The minimal spanning tree problem is to connect all nodes in a network so that the total branch lengths are minimized. Answer: TRUE Diff: 1 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

11) The first step of the minimal spanning tree solution to compute the distance of any path through the network. Answer: FALSE Diff: 2 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

12) The last step of the minimal spanning tree solution method is to make sure all nodes have joined the spanning tree. Answer: TRUE Diff: 2 Page Ref: 307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

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13) In a minimal spanning tree, the source and destination nodes must be connected along a single path. Answer: FALSE Diff: 1 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

14) The choice of the initial node in the minimal spanning tree technique must be the first node. Answer: FALSE Diff: 1 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

15) The minimal spanning tree allows the visitation of each node without backtracking. Answer: FALSE Diff: 2 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

16) The shortest route network problem could help identify the best plan for running cables for televisions throughout a building. Answer: FALSE Diff: 2 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: network flow models, shortest route, minimal spanning tree AACSB: Analytical thinking

17) Regardless of the number of nodes in a network, the minimal spanning tree always contains the two nodes with the shortest distance between them. Answer: TRUE Diff: 2 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Application of knowledge

18) Regardless of the number of nodes in a network, the minimal spanning tree cannot contain the two nodes with the greatest distance between them. Answer: FALSE Diff: 2 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

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19) The goal of the maximal flow problem is to maximize the amount of flow of items from an origin to a destination. Answer: TRUE Diff: 1 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Application of knowledge

20) The shortest route problem requires that there be a branch from each destination to every other destination. Answer: FALSE Diff: 1 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: maximal flow problem AACSB: Application of knowledge

21) The maximal flow algorithm may end with capacity remaining at the source. Answer: FALSE Diff: 2 Page Ref: 312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

22) The source node is the input node in a maximal flow problem. Answer: TRUE Diff: 1 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Application of knowledge

23) The maximal flow solution algorithm allows the user to choose a path through the network from the origin to the destination by any criteria. Answer: TRUE Diff: 1 Page Ref: 310 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem, solution of the maximal flow problem AACSB: Analytical thinking

24) A traffic system could be represented as a network in order to determine bottlenecks using the maximal flow network algorithm. Answer: TRUE Diff: 1 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: network flow models, maximal flow AACSB: Analytical thinking

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25) In a network flow problem, ________ represent junction points connecting branches. Answer: nodes Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow models, nodes AACSB: Application of knowledge

26) In a network flow problem, ________ connect nodes and show flow from one point to another. Answer: branches Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow models, branches AACSB: Application of knowledge

27) In a network flow problem, the values assigned to ________ typically represent distance, time, or cost. Answer: branches Diff: 1 Page Ref: 297 Section Heading: Network Components Keywords: network flow models, branches AACSB: Application of knowledge

28) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the ________ solution technique. Answer: shortest route Diff: 1 Page Ref: 297 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

29) The ________ connects all nodes in a network so that the total branch lengths are minimized. Answer: minimal spanning tree Diff: 1 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

30) The goal of the ________ problem is to maximize the amount of flow of items from an origin to a destination. Answer: maximal flow Diff: 1 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Application of knowledge

31) A ________ network model could be used to represent the capacity of a series of dams for flood control. Answer: maximal flow Diff: 2 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: network flow models, maximal flow AACSB: Application of knowledge

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32) A courier service located at the south edge of downtown dispatches three bicycle couriers with identical sets of architectural renderings that must go to three different downtown law offices as quickly as possible. This problem is a likely candidate for analysis using ________. Answer: the shortest route solution/algorithm Diff: 2 Page Ref: 297 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

33) The shortest route problem formulation requires a statement that mandates that what goes in to a node must equal what comes out of that node. This is referred to as ________. Answer: conservation of flow Diff: 2 Page Ref: 302 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

34) A company plans to use an automatic guided vehicle for delivering mail to ten departments. The vehicle will begin from its docking area, visit each department, and return to the docking area. Cost is proportional to distance traveled. The type of network model that best represent this situation is ________. Answer: shortest route Diff: 2 Page Ref: 297 Section Heading: The Shortest Route Problem Keywords: network flow models, shortest route AACSB: Analytical thinking

35) Determining where to build roads at the least cost within a park that reaches every popular sight represents a ________ network model. Answer: minimal spanning tree Diff: 1 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: network flow models, minimal spanning tree AACSB: Analytical thinking

36) A one-way street in a downtown area should be modeled as a(n) ________ branch in a maximal flow model. Answer: directed Diff: 1 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: directed branch AACSB: Application of knowledge

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37) In a typical network flow problem, the branches show flow from one node to the next. The nodes themselves are ________ points. Answer: junction (connecting) Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow models, nodes AACSB: Application of knowledge

38) Once a decision maker has determined the shortest route to any node in the network, that node becomes a member of the ________. Answer: permanent set Diff: 1 Page Ref: 298 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Application of knowledge

39) Determining where to build one way roads at the least cost within a park that takes visitors to every popular sight and returns them to the entrance represents a ________ network model. Answer: shortest route Diff: 2 Page Ref: 297 Section Heading: The Shortest Route Problem Keywords: network flow models, shortest route AACSB: Analytical thinking

40) Determining where capacity needs to be added within a series of one-way roads within a park represents a ________ model. Answer: maximal flow Diff: 2 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: network flow models, maximal flow AACSB: Analytical thinking

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Figure 1. Delivery Routes 41) Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 2, 3, and 4? Indicate the total distance for each route. Answer: (node 1) - (node 2): 6 miles (node 1) - (node 2) - (node 3): 8 miles (node 1) - (node 2) - (node 4): 11 miles Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

42) Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 5 and 6? Indicate the total distance for each route. Answer: (node 1) - (node 2) - (node 3) - (node 5) : 13 miles (node 1) - (node 2) - (node 4) - (node 6): 13 miles Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

43) Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. Also assume that it is not possible to travel from a node with a higher number to a node with a lower number. Write the constraint associated with the second node (node 2) for the 0-1 integer linear programming formulation of the shortest route problem. Answer: X12 - X24 - X23 = 0 Diff: 2 Page Ref: 302-303 Section Heading: The Shortest Route Problem Keywords: short route prob, integer linear prog form of the short route prob AACSB: Analytical thinking

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44) Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. Also assume that it is not possible to travel from a node with a higher number to a node with a lower number. Write the constraint associated with the fifth node (node 5) for the 0-1 integer linear programming formulation of the shortest route problem. Answer: X35 + X45 - X46 = 0 Diff: 2 Page Ref: 302-303 Section Heading: The Shortest Route Problem Keywords: short route prob, integer linear prog form of the short route prob AACSB: Analytical thinking

45) Consider the network diagram given in Figure 1. Assume that the numbers on the branches indicate the length of cable (in miles) between each pair of the six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes? Answer: 17 miles Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal span tree prob, solution of minimal span tree prob AACSB: Analytical thinking

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Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in the figure below shows the possible routes and travel times (in minutes) from the carpet plant to the various warehouses or retail outlets.

V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Merillville, L = Lansing 46) Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso, Indiana, to warehouses in Hammond, Gary, and Merillville. State the total completion time in minutes or each route. Answer: Valparaiso - Portage - Merillville: 19 minutes Valparaiso - Portage - Gary: 25 minutes Valparaiso - Portage - Merillville - Hammond: 30 minutes Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

47) Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso, Indiana, to retail outlets in Portage, Highland, and Lansing. State the total completion time in minutes or each route. Answer: Valparaiso - Portage: 13 minutes Valparaiso - Portage - Merillville - Hammond - Highland: 35 minutes Valparaiso - Portage - Merillville - Hammond - Lansing: 37 minutes Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

48) Write the constraint associated with the Valparasio (source) node for the 0-1 integer linear programming formulation of the shortest route problem. Answer: XVP + XVM = 1 Diff: 2 Page Ref: 302-303 Section Heading: The Shortest Route Problem Keywords: short route prob, integer linear prog form of the short route prob AACSB: Analytical thinking

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49) Write the constraint associated with the Lansing (destination) node for the 0-1 integer linear programming formulation of the shortest route problem. Answer: XHi-L + XHa-L = 1 Diff: 2 Page Ref: 302-303 Section Heading: The Shortest Route Problem Keywords: short route prob, integer linear prog form of the short route prob AACSB: Analytical thinking

50) Draw the network associated with the following constraints for a shortest route problem. X12 + X13 = 1 X12 - X24 = 0 X13 - X34 = 0 X24 + X34 - X45 = 0 X45 = 1 Answer:

Diff: 3 Page Ref: 302-303 Section Heading: The Shortest Route Problem Keywords: network flow problem, shortest route AACSB: Analytical thinking

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Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility.

51) Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built. Answer: Minimal spanning tree shown in bold.

Diff: 1 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

52) The camp nurse is stationed at Facility B. What is the shortest route from B to C? Answer: B to G to E to C for a total of 30. Diff: 1 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

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Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E.

53) Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built. Answer: Minimal spanning tree shown in bold.

Diff: 1 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

54) A clean-up crew is stationed at facility D and wants to take the shortest route to each site. They usually clean up facilities C, E, A and F on the same day and therefore want the shortest route from D to each facility. Recommend a route for the crew to leave from D, clean up each facility one after the other, and return to facility D. (Assume all paths are accessible.) Answer: D to E to F to C to A to D. Total distance = 47. This is really a small version of the traveling salesman problem. Doing the minimal spanning tree prior to this problem may be helpful. Diff: 2 Page Ref: 291-298 Section Heading: Network Models Keywords: shortest route problem AACSB: Analytical thinking

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55) A clean-up crew is stationed at facility F and wants to take the shortest route to each site. They usually clean up facilities B and A on the same day and therefore want the shortest route from F to each facility. Recommend a route for the crew to leave from F, clean up each facility A and B, and then return to facility F. (Assume all paths are accessible.) Answer: F-E-G-B-D-A-C-F for a total of 77. (This is a small version of the traveling salesmen problem. Doing the minimal spanning tree prior to this problem may be helpful.). The clean-up crew may want to add additional facilities on the days they clean up A and B if they have time. Diff: 2 Page Ref: 291-298 Section Heading: Network Models Keywords: shortest route problem AACSB: Analytical thinking

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Comedy Pasture A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in.

56) The llamas are interested in developing a series of llama-only paths among their points of interest. As they have a limited budget, they'd prefer to develop those paths using a minimum quantity of materials and labor. Which of the point to point paths should be used and what is the total path distance? Answer: The paths are: Fruit-Barn = 20' Barn-Oak = 80' Oak-Hay = 60' Hay-Shade = 50' Hay-Pond = 60' The total path distance is 270' Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

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57) The llamas are interested in developing a series of llama-only paths among their points of interest. As they have a limited budget, they'd prefer to develop those paths using a minimum quantity of materials and labor. Formulate an objective function for this scenario using a linear programming model. Answer: Decision variables are represented by an alphabetic ordering of the two node, e.g., the BarnFruit path is decision variable BF. Min Z = 20BF + 80BO + 110BS + 95FO + 300FP + 60HO + 60HP + 50HS + 90OP + 70OS Diff: 1 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

58) Llamas are pack animals and the owner occasionally has them tote supplies from the barn to the fruit trees, oak trees, hay stand, shade area and down to the pond. What is the shortest route from the barn to these five other locations? Answer: The shortest distance from the Barn to each destination is shown in the table: From Barn to Fruit Oak Shade Hay Pond

Distance 20' 80' 110' 140' 170'

Route direct direct direct Oak-Hay Oak-Pond

Diff: 1 Page Ref: 298-299 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

59) The horse is interested in developing a series of horse-only paths (named The Caballo Real) among its points of interest. The horse has a small budget and no one to help her, so it would prefer to develop those paths using a minimum quantity of materials and labor. Which of the point to point paths should be used and what is the total distance? Answer: The paths needed are: Pond-Hay = 60' Hay-Oak = 60' Oak-Barn = 80' Barn-Grass = 70' Total path distance is 270' Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

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60) The horse isn't crazy about it, but occasionally will relent and pull a cart laden with supplies from the barn to the other points of mutual interest, the grassy area, the pond, and the hay down in the run in shed. What is the shortest distance from the barn to each of these points? Answer: The distance and route from the barn are given in this table: From the Barn to Grass Hay Pond

Distance 70' 140' 170'

Route direct Oak-Hay Oak-Pond

Diff: 1 Page Ref: 298-299 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

61) The horse and llamas decide to join forces to develop a series of paths among their points of interest. All of them are spenders rather than savers, so they prefer to develop those paths using a minimum quantity of materials and labor. Which of the point to point paths should be used and what is the total distance? Answer: Fruit-Barn = 20' Barn-Grass = 70' Barn-Oak = 80' Oak-Hay = 60' Hay-Shade = 50' Hay-Pond = 60' Total path distance is 340' Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

62) During the harvest, the horse and llamas are herded up to the orchard where they are loaded down with fresh-picked fruit. Some of the fruit is taken to the pond to feed the catfish and the remainder is crated up underneath the shade trees. What is the shortest route to those locations; provide distance and the path? Answer: From the fruit trees, the shortest route to the pond is 185' from Fruit to Oak to Pond. The shortest route to the Shade is 130' from Fruit to Barn to Shade. Diff: 1 Page Ref: 298-299 Section Heading: The Shortest Route Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

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Comedy Pasture II A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. This map shows the number of loads that can be hauled between all connected points on the property. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in.

63) The horse spoke up first, "I'm twice your size and can work twice as hard. It doesn't matter how much needs to be hauled from the grassy area in the comedy pasture down to the pond, I can do it easily in a day." Of course, the horse would use only routes connected by his nodes of interest, Grass, Barn, Oak, Hay and Pond. Use the capacities indicated on each of the branches to determine the maximal flow down to the pond. Answer: The maximum flow is 14 using these paths: Grass-Hay = 6, continuing on Hay-Pond Grass-Oak = 8, continuing on Oak-Pond Diff: 2 Page Ref: 310-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

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64) The llamas took pride in the centuries old use as pack animals in the South American Andes. Using only their network of nodes, Fruit, Barn, Grass, Oak, Shade, Hay and Pond, they figured they could easily outhaul the horse. Use the capacities indicated on each of the branches to determine the maximal flow from the Barn down to the pond. Answer: The maximum flow is 20 using these paths: Barn - Oak - Pond = 8 Barn - Oak - Hay - Pond = 2 Barn - Shade - Oak - Fruit - Pond = 5 Barn - Fruit Oak - Shade - Hay - Pond = 5 Diff: 2 Page Ref: 310-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

65) The llamas took pride in the centuries old use as pack animals in the South American Andes. They decided to join forces with their grazing buddy the horse and lug ripe fruit from the orchard (designated as Fruit) down to the Pond. Use the capacities indicated on each of the branches to determine the maximal flow from the orchard down to the pond. Answer: The maximum flow is 23 using these paths: Fruit-Pond = 5 Fruit-Barn-Grass-Oak-Pond = 8 Fruit-Oak-Grass-Hay-Pond = 7 Fruit-Barn-Oak-Shade-Hay-Pond = 3 Diff: 3 Page Ref: 310-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

66) The llamas took pride in the centuries old use as pack animals in the South American Andes. They decided to join forces with their grazing buddy the horse and lug hay from the Barn down to the area designated as Hay for long term storage. Use the capacities indicated on each of the branches to determine the maximal flow from the Barn down to Hay. Answer: The maximum flow is 20 using these paths: Barn-Grass-Hay = 7 Barn-Oak-Hay = 6 Barn-Fruit-Oak-Shade-Hay = 5 Diff: 3 Page Ref: 310-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

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Refer to the figure below to answer the following questions.

Figure 3 67) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9. Answer: maximum flow: 12 Diff: 3 Page Ref: 309-313 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem, solution of the maximal flow problem AACSB: Analytical thinking

68) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 2 to node 7 to destination node 9. Answer: maximum flow: 5 Diff: 2 Page Ref: 309-313 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem, solution of the maximal flow problem AACSB: Analytical thinking

69) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the objective function for the 0-1 integer linear programming formulation of the maximal flow problem? Answer: maximize Z = X91 Diff: 3 Page Ref: 313 Section Heading: The Maximal Flow Problem Keywords: max flow prob, 0-1 integer linear prog formulation of the max flow prob AACSB: Analytical thinking

70) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input- output constraint associated with the first node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem? Answer: X91 - X12 - X13 - X14 = 0 Diff: 3 Page Ref: 313-314 Section Heading: The Maximal Flow Problem Keywords: max flow prob, 0-1 integer linear prog formulation of the max flow prob AACSB: Analytical thinking

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71) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input-output constraint associated with the ninth node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem? Answer: X79 + X89 - X91 = 0 Diff: 3 Page Ref: 313-314 Section Heading: The Maximal Flow Problem Keywords: max flow prob, 0-1 integer linear prog formulation of the max flow prob AACSB: Analytical thinking

72) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the capacity constraint associated with the branch from node 7 to node 9 of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem? Answer: X79 ≤ 8 Diff: 3 Page Ref: 313-314 Section Heading: The Maximal Flow Problem Keywords: max flow prob, 0-1 integer linear prog formulation of the max flow prob AACSB: Analytical thinking

73) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input-output constraint associated with the fifth node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem? Answer: X25 + X35 + X65 - X56 - X57 = 0 Diff: 3 Page Ref: 313-314 Section Heading: The Maximal Flow Problem Keywords: max flow prob, 0-1 integer linear prog formulation of the max flow prob AACSB: Analytical thinking

74) Using the network shown and the conventional method discussed in your textbook, what are the first two nodes in the network and why? Now avoid convention and pick the first two nodes that must be part of the correct solution. Why is this the case? Answer: Convention dictates that a solution begins with node 1 and proceeds to the nearest node, which is node 3 at a distance of 11. Tossing convention out, one should pick the two closest nodes, which in this network are nodes 4 and 5, separated by only 6 units. Diff: 3 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

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75) If the origin node for this network is node number 1 and flow proceeds from node 1 to node 6, what is the shortest route through the network? Answer: 1-3-6 = 21 Diff: 1 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

76) The origin node for this network is node number 1 and flow proceeds from node 1 to node 6. If the distance from node three to node six doubles , what is the change in the shortest route through the network? Answer: The shortest route changes from 1-3-6=21 to 1-4-5-6=29, so a total increase of 8. Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

77) The origin node for this network is node number 1 and flow proceeds from node 1 to node 6. If each of the three longest branches is reduced in length by 10, what is the change in the shortest route through the network? Answer: The shortest route changes from 1-3-6=21 to 1-2-5-6=18 for a total decrease of 3. Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

78) Consider the network shown in the figure. The architect decides to remove a few of the (undirected) arcs but still have each node connected to at least one other node within a single network. Which arcs should be removed and what is the total arc length that is removed? Answer: The arcs to be removed are arcs 1-2=13, 2-5=17, 3-6=10, 1-4=15, for a total arc length removed of 13+17+10+15=55 units. The remaining arc length is 40. Not too shabby! Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

79) In a network flow model, a directed branch: A) is a branch with a positive distance value. B) is a branch in which flow is possible in only one direction. C) is a branch on which the flow capacity is exhausted. D) is a branch in which flow is not possible in either direction. Answer: B Diff: 2 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: directed branch AACSB: Application of knowledge

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80) In a network modeling problem, the linear programming decision variables are given by: A) source node. B) sink node. C) network branches. D) network nodes. Answer: C Diff: 2 Page Ref: 296 Section Heading: Network Components Keywords: network flow model, linear programming decision variables AACSB: Application of knowledge

81) A branch where flow is permissible in either direction is a(n): A) directed branch. B) undirected branch . C) labeled branch. D) unlabeled branch. Answer: B Diff: 2 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: network flow model, branches AACSB: Application of knowledge

82) If we wanted to represent water resources as a network flow problem, which of the following would be represented as nodes? A) canals B) pumping stations C) rivers D) pipelines Answer: B Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow model AACSB: Application of knowledge

83) If we wanted to represent an office layout as a network flow problem, which of the following would be represented as a branch? A) offices B) waiting areas C) heating and ventilation systems D) computer rooms Answer: C Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow model AACSB: Application of knowledge

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84) If we wanted to represent an urban transportation system as a network flow problem, which of the following would be represented as nodes? A) streets B) railway lines C) street intersections D) pedestrian right of ways Answer: C Diff: 1 Page Ref: 296 Section Heading: Network Components Keywords: network flow model AACSB: Application of knowledge

85) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the: A) shortest route solution technique. B) minimal spanning tree solution method. C) maximal flow solution method. D) minimal flow solution method. Answer: A Diff: 2 Page Ref: 298 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

86) In the linear programming formulation of the shortest route problem, the constraint for each node represents: A) capacity on each path. B) conservation of flow. C) capacity on each branch. D) minimum flow. Answer: B Diff: 2 Page Ref: 302 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

87) The first step in the shortest route solution method is to: A) select the node with the shortest direct route from the origin. B) determine all nodes directly connected to the permanent set nodes. C) arbitrarily select any path in the network from origin to destination. D) make sure that all nodes have joined the permanent set. Answer: A Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Application of knowledge

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Figure 2 88) Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (node 1) to node 4? A) 8 B) 9 C) 10 D) 11 Answer: D Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

89) Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (node 1) to node 5? A) 13 B) 14 C) 15 D) 16 Answer: A Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

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Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in figure below shows the possible routes and distances from the carpet plant in Valparaiso to the various warehouses or retail outlets.

V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Merillville, L = Lansing 90) What is the distance for the shortest route from the carpet plant in Valparaiso to retail outlet in Lansing, Illinois. State the total completion time in minutes. A) 36 B) 37 C) 39 D) 41 Answer: A Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

91) Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso to retail outlet in Hammond. A) 26 B) 28 C) 30 D) 32 Answer: B Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem, shortest route problem solution AACSB: Analytical thinking

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92) The minimal spanning tree problem determines the: A) minimum amount that should be transported along any one path. B) maximum amount that can be transported along any one path. C) shortest distance between a source node and a destination node. D) minimum total branch lengths connecting all nodes in the network. Answer: D Diff: 2 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

93) The first step of the minimal spanning tree solution method is to: A) select any starting node. B) select the node closest to the starting node to join the spanning tree. C) select the closest node not presently in the spanning tree. D) arbitrarily select any path in the network from origin to destination. Answer: A Diff: 2 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Application of knowledge

94) The local Internet provider wants to develop a network that will connect its server at its satellite center in Valparaiso with the main city computer centers in Northwest Indiana to improve the Internet service and to minimize the amount of cable used to connect network nodes. If we represent this problem with a network: A) the cities are branches and cables are nodes. B) the cables are the branches and the cities are the nodes. C) the length of cables in miles are the branches, and the cities are the nodes. D) the cities are the branches and the length of cables in miles are the nodes. Answer: C Diff: 2 Page Ref: 305 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

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Figure 2 95) Consider the network diagram given in Figure 2. Assume that the numbers on the branches indicate the length of cable (in miles) six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes? A) 16 miles B) 17 miles C) 18 miles D) 19 miles Answer: C Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal span tree prob, solution of minimal span tree prob AACSB: Analytical thinking

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96) Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. What is the minimum number of paths (in tens of yards) that must be built to connect each facility? A) 54 B) 56 C) 60 D) 65 Answer: A Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

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97) Llamas are pack animals and the owner occasionally has them tote supplies from the fruit trees down to the hay stand. What is the shortest route between the two? A) 150' B) 155' C) 160' D) 165' Answer: B Diff: 1 Page Ref: 298-300 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

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98) Which of these routes for the horse is actually the shortest between the pair of nodes? A) Fruit - Hay = 160' B) Barn - Pond = 200' C) Grass - Pond = 190' D) Fruit - Shade = 165' Answer: C Diff: 1 Page Ref: 298-300 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

99) The horse walks from the Grass to the Pond and the llamas walk from the Fruit to the Shade. How much longer does the horse walk if each takes the shortest possible route? A) 60' B) 50' C) 40' D) 35' Answer: A Diff: 1 Page Ref: 298-300 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

100) The horse decides that a small system of trails would be perfect for connecting his points of interest, the Grass, Barn, Hay and Pond along with the Oak. What is the minimal total path length for this construction project? A) 295' B) 290' C) 280' D) 270' Answer: D Diff: 1 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

101) The llamas decide that a small system of trails would be perfect for connecting their points of interest, the Fruit, Barn, Hay, Shade, Pond and the Oak. What is the minimal total path length for this construction project? A) 275' B) 270' C) 265' D) 260' Answer: B Diff: 1 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

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102) The llamas and horse spend most of their day wandering back and forth among their favorite spots in the yard, and have worn paths that are two feet wide among them. Amazingly, these paths correspond to a minimal spanning tree network! The property owner is fearful that the bare dirt paths will wash out during heavy rains, so he initiates a soil conservation project to lay sod over all of the bare dirt paths. How many square feet of sod must he purchase? A) 1080 B) 540 C) 680 D) 820 Answer: C Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree problem AACSB: Analytical thinking

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103) Using the nodes of interest for the llamas, Fruit, Barn, Oak, Shade, Hay and Pond, what is the maximal flow from the Barn to the Pond? A) 17 B) 18 C) 20 D) 23 Answer: C Diff: 2 Page Ref: 310-313 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

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104) Using the nodes of interest for the llamas, Fruit, Barn, Oak, Shade, Hay and Pond, what is the maximal flow from the Fruit to Hay? A) 11 B) 12 C) 13 D) 14 Answer: A Diff: 2 Page Ref: 310-313 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

105) Using the nodes of interest for the horse, Grass, Barn, Oak, Hay and Pond, what is the maximal flow from the Grass to Pond? A) 11 B) 12 C) 13 D) 14 Answer: D Diff: 2 Page Ref: 310-313 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

106) Using the nodes of interest for the horse, Grass, Barn, Oak, Hay and Pond, what is the maximal flow from the Grass to Hay? A) 11 B) 12 C) 13 D) 14 Answer: C Diff: 2 Page Ref: 310-313 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

107) Using all the nodes of interest for the entire menagerie, what is the maximal flow from Fruit to Hay? A) 16 B) 18 C) 20 D) 22 Answer: B Diff: 3 Page Ref: 310-313 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

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108) Using all the nodes of interest for the entire menagerie, what is the maximal flow from Grass to Pond? A) 20 B) 21 C) 22 D) 23 Answer: B Diff: 3 Page Ref: 310-313 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

109) The objective of the maximal flow solution approach is to: A) maximize resource allocation . B) maximize the total amount of flow from an origin to a destination. C) determine the longest distance between an originating point and one or more destination points. D) determine the shortest distance between an originating point and one or more destination points. Answer: B Diff: 2 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Application of knowledge

110) The first step of the maximal flow solution method is to: A) arbitrarily select any path in the network from origin to destination. B) select the node with the shortest direct route from the origin. C) add the maximal flow along the path to the flow in the opposite direction at each node. D) select any starting node. Answer: A Diff: 2 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Application of knowledge

111) The shortest route problem requires: A) each destination to be visited only once. B) finding the quickest route from the source to each node. C) that there be a branch from each destination to every other destination. D) that there be no two-way branches between nodes. Answer: B Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Application of knowledge

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112) The maximal flow algorithm: A) does not require flow on every branch for the final solution. B) may end with capacity remaining at the source. C) may end with capacity at those nodes leading immediately to the destination. D) all of the above Answer: D Diff: 2 Page Ref: 309 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

Refer to the figure below to answer the following questions.

Figure 3 113) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9. A) 10 B) 11 C) 12 D) 13 Answer: C Diff: 2 Page Ref: 309-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem, solution of the maximal flow problem AACSB: Analytical thinking

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114) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 4 to node 3 to node 5 to node 8 to destination node 9. A) 2 B) 3 C) 4 D) 5 Answer: A Diff: 2 Page Ref: 309-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem, solution of the maximal flow problem AACSB: Analytical thinking

115) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 2 to node 7 to destination node 9. A) 3 B) 4 C) 5 D) 6 Answer: C Diff: 2 Page Ref: 309-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem, solution of the maximal flow problem AACSB: Analytical thinking

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Figure 4 116) Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches. A) 10 B) 11 C) 13 D) 16 Answer: C Diff: 2 Page Ref: 309-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem AACSB: Analytical thinking

117) Determine the minimum distance required to connect all nodes in Figure 4. A) 22 B) 24 C) 26 D) 30 Answer: C Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

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118) Which of these is the shortest route through the network? A) 1-3-6 B) 1-2-5-6 C) 1-4-5-6 D) 1-2-4-5-6 Answer: A Diff: 1 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

119) This network has been targeted for the innovative new "Redundancy Elimination" program that offers a compromise between two competing factions. The plan is to remove paths one at a time until all of the nodes are interconnected without any loops in the network while minimizing the sum of all of the path lengths. Which of these paths is part of the new network? A) 3-6 B) 1-3 C) 1-2 D) 2-5 Answer: B Diff: 1 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

120) How much longer is the total arc length in the current network than twice the total arc length of the minimal spanning tree? A) 5 B) 10 C) 15 D) 20 Answer: C Diff: 2 Page Ref: 305-307 Section Heading: The Minimal Spanning Tree Problem Keywords: minimal spanning tree AACSB: Analytical thinking

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121) If the two shortest paths in this network are increased by 100%, and the two longest paths in this network are reduced by 50%, what is the shortest route through this network? A) 10.5 B) 17.5 C) 19.5 D) 21 Answer: D Diff: 2 Page Ref: 298-301 Section Heading: The Shortest Route Problem Keywords: shortest route problem AACSB: Analytical thinking

122) Use the network pictured and assume all labeled flows are forward flows. Suppose the reverse flows for each path are exactly half of the forward flows. What is the maximum flow through this network? A) 18 B) 28 C) 10 D) 8 Answer: A Diff: 2 Page Ref: 309-312 Section Heading: The Maximal Flow Problem Keywords: maximal flow problem, solution of the maximal flow problem AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 8 Project Management 1) Project teams are made up of individuals from various areas and departments within a company. Answer: TRUE Diff: 1 Page Ref: 349 Section Heading: The Elements of Project Management Keywords: project management, project teams AACSB: Application of knowledge

2) A statement of work is a written description of the goals, work, and time frame of a project. Answer: TRUE Diff: 1 Page Ref: 350 Section Heading: The Elements of Project Management Keywords: project management AACSB: Application of knowledge

3) The sequence of activities in a project is depicted by the precedence relationships. Answer: TRUE Diff: 2 Page Ref: 349 Section Heading: The Elements of Project Management Keywords: precedence relationship AACSB: Application of knowledge

4) A work breakdown structure breaks down a project into subcomponents, components, activities, and tasks. Answer: TRUE Diff: 2 Page Ref: 350 Section Heading: The Elements of Project Management Keywords: a work breakdown structure AACSB: Application of knowledge

5) An element of project planning is to compare the project schedule objectives. Answer: TRUE Diff: 1 Page Ref: 347 Section Heading: The Elements of Project Management Keywords: project planning AACSB: Application of knowledge

6) Determining project completion time is an element of project planning. Answer: TRUE Diff: 1 Page Ref: 347 Section Heading: The Elements of Project Management Keywords: project completion time, project planning AACSB: Application of knowledge

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7) One aspect of project control is team building. Answer: FALSE Diff: 1 Page Ref: 347 Section Heading: The Elements of Project Management Keywords: project planning AACSB: Application of knowledge

8) The critical path is the shortest path through the project network. Answer: FALSE Diff: 1 Page Ref: 352 Section Heading: CPM/Pert Keywords: project network, critical path AACSB: Application of knowledge

9) The critical path is the longest path through the project network. Answer: TRUE Diff: 1 Page Ref: 352 Section Heading: CPM/Pert Keywords: project network, critical path AACSB: Application of knowledge

10) Slack is the amount of time an activity can be delayed without delaying the project. Answer: TRUE Diff: 1 Page Ref: 354 Section Heading: The Elements of Project Management Keywords: project network, slack AACSB: Application of knowledge

11) In PERT, three time estimates (optimistic, most likely, and pessimistic) provide an estimate of the mean and variance for each activity, based on the normal distribution. Answer: FALSE Diff: 1 Page Ref: 358 Section Heading: Project Networks Keywords: project network, beta distribution AACSB: Application of knowledge

12) The critical path activities have no slack. Answer: TRUE Diff: 1 Page Ref: 350 Section Heading: CPM/Pert Keywords: project network, critical path activities AACSB: Application of knowledge

13) In PERT, the project variance is the sum of the variance of all project activities. Answer: FALSE Diff: 1 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: project network, project variance AACSB: Analytical thinking

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14) In PERT, the expected project completion time is assumed to be distributed according to a beta distribution. Answer: FALSE Diff: 1 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: project network, normal distribution AACSB: Analytical thinking

15) The expected project completion time is assumed to be normally distributed. Answer: TRUE Diff: 1 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: project network, normal distribution AACSB: Analytical thinking

16) Project crashing is a method for shortening the project completion time by reducing the completion time of one or more critical activities at a cost. Answer: TRUE Diff: 1 Page Ref: 376 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: project network, crashing AACSB: Application of knowledge

17) An AON network will never require dummy activities. Answer: TRUE Diff: 1 Page Ref: 350 Section Heading: CPM/Pert Keywords: project network, AON network AACSB: Application of knowledge

18) Two concurrent activities in a project can be represented in an AOA network by starting and ending on the same node. Answer: FALSE Diff: 1 Page Ref: 351 Section Heading: CPM/Pert Keywords: project network, AOA network AACSB: Application of knowledge

19) The early start for an activity on the critical path is always equal to the earliest finish of the preceding activity. Answer: TRUE Diff: 1 Page Ref: 353 Section Heading: CPM/Pert Keywords: project network, critical path AACSB: Analytical thinking

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20) The early start for a non-critical activity is always equal to the earliest finish of the preceding activity. Answer: FALSE Diff: 1 Page Ref: 353 Section Heading: CPM/Pert Keywords: project network, non critical activities AACSB: Analytical thinking

21) The early finish for an activity on the critical path is equal to the latest finish of the preceding activity. Answer: FALSE Diff: 1 Page Ref: 353 Section Heading: CPM/Pert Keywords: project network, critical path AACSB: Analytical thinking

22) A work breakdown structure is a useful tool because it addresses the timing of individual work elements. Answer: FALSE Diff: 2 Page Ref: 350 Section Heading: The Elements of Project Management Keywords: project planning AACSB: Application of knowledge

23) The PERT pessimistic time estimate is an estimate of the minimum time an activity will require. Answer: FALSE Diff: 1 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: project network, PERT AACSB: Analytical thinking

24) The standard deviation of project duration is the average of the standard deviation of all activities on the critical path. Answer: FALSE Diff: 2 Page Ref: 360-362 Section Heading: CPM/Pert Keywords: project network, PERT AACSB: Analytical thinking

25) When earliest finish is subtracted from latest finish, we obtain the slack value for the activity. Answer: TRUE Diff: 1 Page Ref: 356 Section Heading: CPM/Pert Keywords: slack AACSB: Analytical thinking

26) Shortening the project's duration by deleting unnecessary activities is called crashing. Answer: FALSE Diff: 1 Page Ref: 376 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: project network, crashing AACSB: Application of knowledge

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27) The earliest finish time for the final activity on a project network is also the total completion of the project. Answer: TRUE Diff: 1 Page Ref: 354-355 Section Heading: CPM/Pert Keywords: project network, PERT/CPM solution AACSB: Application of knowledge

28) The early start of an activity that has only one predecessor is equal to the early finish of that predecessor. Answer: TRUE Diff: 1 Page Ref: 353 Section Heading: CPM/Pert Keywords: project planning AACSB: Application of knowledge

29) The early start of an activity that has more than one predecessor is the minimum of the earliest finishes of all predecessors. Answer: FALSE Diff: 2 Page Ref: 353 Section Heading: CPM/Pert Keywords: early start AACSB: Analytical thinking

30) Project ________ is a method for shortening the project completion time by reducing the completion time of one or more critical activities at a cost. Answer: crashing Diff: 1 Page Ref: 376 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: project network, crashing AACSB: Application of knowledge

31) The expected project completion time is assumed to be ________ distributed based on the central limit theorem. Answer: normally Diff: 1 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: project network, normal distribution AACSB: Application of knowledge

32) Three time estimates (optimistic, most likely, and pessimistic) provide an estimate of the mean and variance for each activity, based on the ________ distribution. Answer: beta Diff: 1 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: project network, beta distribution AACSB: Application of knowledge

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33) ________ is the amount of time an activity can be delayed without delaying the project. Answer: Slack Diff: 1 Page Ref: 356 Section Heading: CPM/Pert Keywords: project network, slack AACSB: Application of knowledge

34) A(n) ________ chart is a graph or a bar chart for each activity that shows the project schedule and the passage of time. Answer: Gantt chart Diff: 1 Page Ref: 346 Section Heading: Project Networks Keywords: project network, Gantt chart AACSB: Application of knowledge

35) In an AOA network, a ________ activity is used to show a precedence relationship, but it does not represent passage of time. Answer: dummy Diff: 1 Page Ref: 350 Section Heading: CPM/Pert Keywords: project network, dummy activities AACSB: Application of knowledge

36) When the earliest start time (ES) of an activity is subtracted from the latest start time (LS) of an activity, the value obtained is called ________. Answer: slack Diff: 1 Page Ref: 356 Section Heading: CPM/Pert Keywords: project network, PERT/CPM solution AACSB: Analytical thinking

37) A ________ breaks down a project into modules: subcomponents, components, activities, and tasks. Answer: word breakdown structure Diff: 1 Page Ref: 350 Section Heading: The Elements of Project Management Keywords: work breakdown structure AACSB: Application of knowledge

38) When applying linear programming models to project crashing, the objective is to minimize ________. Answer: the cost of crashing Diff: 2 Page Ref: 381 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: crashing, linear programming AACSB: Application of knowledge

6 .

39) When applying linear programming models to project planning, the objective is to minimize ________. Answer: project duration Diff: 2 Page Ref: 381 Section Heading: Formulating the CPM/Pert Network as a Linear Programming Model Keywords: PERT/CPM, linear programming AACSB: Application of knowledge

Refer to the table below to answer the question(s) that follow:

40) What are the estimated expected completion (mean) times (in weeks) for activities A-H? Answer: (15; 20; 10; 35; 25; 30; 20; 5) Diff: 2 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: estimated expected completion (mean) times AACSB: Analytical thinking

41) What is the critical path for this project network? Answer: ADGH Diff: 2 Page Ref: 352 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

42) If the early start for activity A is equal to 23 months and the duration of activity A is equal to 5 months, what is the earliest finish for activity A? Answer: 28 months Diff: 1 Page Ref: 354 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

43) If the earliest finish for activity C is equal to 10 months and its duration 3 months, what is its earliest start? Answer: 7 months Diff: 2 Page Ref: 353 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

7 .

Refer to the table below to answer the question(s) that follow:

44) Determine the latest start for activity E. Answer: 25 weeks Diff: 2 Page Ref: 355 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

45) What are the estimated slack times (in weeks) for activities A-H? Answer: (0; 5; 15; 0; 5; 15; 0; 0) Diff: 2 Page Ref: 356 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

46) What are the estimated standard deviations (in weeks) in the times for activities A-H? Answer: (2; 1.67; 2; 4; 1.33; 3; 2; 1) Diff: 2 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution AACSB: Analytical thinking

47) What is the estimated expected mean time (in weeks) for the project completion? Answer: 75 Diff: 2 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

48) What is the estimated standard deviation (in weeks) for the critical path completion time? Answer: 5 Diff: 2 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

8 .

49) What is the probability that the critical path for this project will be completed within 75 weeks? Answer: 0.5 Diff: 2 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

50) What is the probability that the critical path for this project will be completed within 80 weeks? Answer: 0.8413 Diff: 2 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

51) Within what amount of time (in weeks) is there a 90% probability that the critical path for this project will be completed? Answer: 81.4 Diff: 2 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

52) Within what amount of time (in weeks) is there a 99% probability that the critical path for this project will be completed? Answer: 86.65 Diff: 2 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

9 .

Project Sand Mandala Carrie meticulously calculated the early and late start and finish times for her latest project and recorded them using different colors of sand on a pristine slab of white marble. She used red for late start and late finish times and green for early start and early finish times. Activity durations and their identifiers were written with black sand. She finished her task and had an opportunity to admire her work only briefly before a colleague came by and swept most of it away. Sadly, this was before Carrie could record the numbers on a more permanent medium, so now she turns to you to help. Activity A B C D E F G H J K

Predecessor A A B B D,E F C G,H,J

Duration

Early Start

Early Finish 10 7

Late Start

15 11

Late Finish 11

7 19

10 24 24 28 36

53) Fill in all of the missing information from the table. Answer: The entire table should appear as follows: Activity A B C D E F G H J K

Pred --A A B B D,E F C G,H,J

Duration 10 7 7 5 4 10 9 7 11 8

Early Start Early Finish 0 10 0 7 10 17 10 15 7 11 7 17 15 24 17 24 17 28 28 36

Diff: 3 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

10 .

Late Start 0 4 10 14 15 11 19 21 17 28

Late Finish 10 11 17 19 19 21 28 28 28 36

54) Fill in all of the missing information for activity A and for activity K. Answer: Activities A and K must both be on the critical path, so A has early and late start times of 0. The early finish for A was given as 10, so its late finish must also be 10, hence its duration must be 10. The late finish for activity K was provided as 36, thus its early finish must be 36. The late finish for activity J, its immediate predecessor, was given as 28, so K's early and late starts must both be 28. K's duration is then 8. Activity A K

Pred -J,G,H

Duration 10 8

Early Start Early Finish 0 10 28 36

Late Start 0 28

Late Finish 10 36

Diff: 1 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

55) What are the early and late start times for activities C, D, E, and F? Answer: Activities A is critical and has an early finish of 10, so C and D must both have an early start of 10. In addition, at least one of these two must have a late start of 10 as the critical path goes through A. D has a late start of 14, so C must be critical, therefore C's late start time is also 10. D has an early finish of 15, so its late finish must be 4 more than its early finish, or 19. D's duration is 5 as the difference of its early start and early finish times. C has a duration of 7, so it must have early and late finish times of 10 + 7 = 17. B's early finish is given as 7 and late finish as 11, so E and F's early start must be 7. E's early finish is given as 11 and late finish as 19. its early start must be 7 from B's early finish, so adding E's slack to the 7 yields a late start for E of 15. E's duration is therefore 4. F's duration is given as 10. With an early start of 7, the early finish must be 17. With B's late finish of 11, then the late start for F is also 11. FG's late finish is 21 as it is 10 more than its late start. Activity A C D E F

Pred -A A B B

Duration 10 7 5 4 10

Early Start Early Finish 0 10 10 17 10 15 7 11 7 17

Diff: 2 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

11 .

Late Start 0 10 14 15 11

Late Finish 10 17 19 19 21

56) Given the following information for a project, draw the AON (Activity-On-Node) project network.

Activity A B C D E F G H

Immediate Processor A, B B C C, D D E, F, G

Activity Time (days) 6 8 5 4 7 3 6 5

Answer:

Diff: 2 Page Ref: 351 Section Heading: CPM/Pert Keywords: project network diagram, AON network AACSB: Analytical thinking

12 .

57) Given the following information for a project, draw the AOA (Activity-On-Arrow) project network.

Activity A B C D E F G H

Immediate Processor A, B B C C, D D E, F, G

Activity Time (days) 6 8 5 4 7 3 6 5

Answer:

Diff: 3 Page Ref: 351 Section Heading: CPM/Pert Keywords: project network diagram, AOA network AACSB: Analytical thinking

13 .

58) Given the following information for a project, identify the critical path and determine the total completion time of the project.

Activity A B C D E F G H

Immediate Processor A, B B C C, D D E, F, G

Activity Time (days) 6 8 5 4 7 3 6 5

Answer: Critical path = BCEH. Project completion time = 25 days. Activity A B C D E F G H

ES 0 0 8 8 13 13 12 20

EF 6 8 13 12 20 16 18 25

LS 2 0 8 10 13 17 14 20

LF 8 8 13 14 20 20 20 25

CP = Critical Path Diff: 2 Page Ref: 351 Section Heading: CPM/Pert Keywords: PERT/CPM solution method AACSB: Analytical thinking

14 .

Slack 2 0 0 2 0 4 2 0

CP No Yes Yes No Yes No No Yes

59) Given the following information for a project, what are the estimated slack times (in weeks) for activities A-H?

Activity A B C D E F G H

Immediate Processor A, B B C C, D D E, F, G

Activity Time (days) 6 8 5 4 7 3 6 5

CP = Critical Path Answer: (A=2; B=0; C=0; D=2; E=0; F=4; G=2; H=0) Activity A B C D E F G H

ES 0 0 8 8 13 13 12 20

EF 6 8 13 12 20 16 18 25

LS 2 0 8 10 13 17 14 20

LF 8 8 13 14 20 20 20 25

Diff: 2 Page Ref: 356 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

15 .

Slack 2 0 0 2 0 4 2 0

CP No Yes Yes No Yes No No Yes

Consider the following network.

60) Identify all paths in the network. Answer: ABDF, ABEF, ACEF, ACG Diff: 1 Page Ref: 350 Section Heading: CPM/Pert Keywords: CPM AACSB: Analytical thinking

61) Identify the critical path. Answer: ABDF Diff: 1 Page Ref: 352 Section Heading: CPM/Pert Keywords: CPM AACSB: Analytical thinking

62) How long will it take to complete the project? Answer: 19 days Diff: 1 Page Ref: 352 Section Heading: CPM/Pert Keywords: CPM AACSB: Analytical thinking

63) Assume that the variance for each activity in the network is equal to 1. Compute the probability that path A-B-E-F will be completed in 15 days. Answer: .50 Diff: 1 Page Ref: 369 Section Heading: Probabilistic Activity Times Keywords: CPM AACSB: Analytical thinking

16 .

The diagram below shows the activities on the nodes, and the table shows the normal time and crash time (in days) and cost for each activity.

Activity

Normal Time

Crash Time

A B C D E F

6 10 5 4 9 2

6 8 4 1 7 1

Cost per day to crash --$100 $300 $700 $500 $650

64) Determine which activities should be crashed to shorten the project by 1 day. Answer: Crash C by 1 day Diff: 2 Page Ref: 377 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: project crashing AACSB: Analytical thinking

65) Determine which activities should be crashed to shorten the project by 2 days. Answer: Crash C by 1 day, E by 1 day Diff: 2 Page Ref: 377 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: project crashing AACSB: Analytical thinking

66) Determine which activities should be crashed to shorten the project by 3 days. What is the cost? Answer: Crash C by 1 day, E by 1 day, and then B by 1 day and E by an additional day. Total cost = $1400. Crash schedule: Path ABF CEDF Cost:

Normal time 18 20

Crash C 18 19 $300

Crash E 18 18 $500

Diff: 2 Page Ref: 377 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: project crashing AACSB: Analytical thinking

17 .

Crash B & E 17 17 $600

67) Once a project is underway, the project manager is responsible for the: A) people. B) cost. C) time. D) all of the above Answer: D Diff: 1 Page Ref: 347 Section Heading: The Elements of Project Management Keywords: elements of project management AACSB: Application of knowledge

68) A work breakdown structure breaks down a project into: A) weeks. B) areas. C) arcs. D) modules. Answer: D Diff: 2 Page Ref: 350 Section Heading: The Elements of Project Management Keywords: elements of project management, work breakdown structure AACSB: Application of knowledge

69) Elements of project planning include: A) defining project objectives. B) identifying activities to crash. C) calculating expected times and standard deviations. D) conducting a "lessons learned" session. Answer: A Diff: 1 Page Ref: 347 Section Heading: The Elements of Project Management Keywords: elements of project planning AACSB: Application of knowledge

70) Elements of project planning include: A) identifying time-cost tradeoffs. B) determining the project critical path. C) comparing project schedule objectives. D) all of the above Answer: C Diff: 1 Page Ref: 347 Section Heading: The Elements of Project Management Keywords: elements of project planning AACSB: Application of knowledge

18 .

71) If an activity cannot be delayed without affecting the entire project, then it is a ________ activity. A) completed B) critical C) crashed D) normal Answer: B Diff: 2 Page Ref: 359 Section Heading: Probabilistic Activity Times Keywords: elements of project planning AACSB: Application of knowledge

72) A list of the tasks, broken down into modules, components, and individual tasks, is called a A) work breakdown structure (WBS). B) PERT. C) planning matrix. D) critical path. Answer: A Diff: 1 Page Ref: 350 Section Heading: The Elements of Project Management Keywords: elements of project management AACSB: Application of knowledge

73) Project control involves: A) crashing. B) three time estimates. C) a backward or forward pass. D) earned value analysis. Answer: D Diff: 2 Page Ref: 355 Section Heading: The Elements of Project Management Keywords: project planning, project control AACSB: Application of knowledge

74) On an AOA diagram, a ________ represents an activity of a project. A) route B) branch C) path D) node Answer: B Diff: 2 Page Ref: 349-350 Section Heading: CPM/Pert Keywords: project network, branches AACSB: Application of knowledge

19 .

75) On an AOA diagram, a ________ represents the beginning and end of activities, referred to as events. A) path B) arc C) branch D) node Answer: D Diff: 2 Page Ref: 349-350 Section Heading: CPM/Pert Keywords: project network, nodes AACSB: Application of knowledge

76) The activities that must be completed prior to the start of an activity in question are called the immediate ________ of the activity in question. A) successors B) predecessors C) successors and predecessors D) followers Answer: B Diff: 1 Page Ref: 349 Section Heading: CPM/Pert Keywords: project network AACSB: Application of knowledge

77) Project management differs from management of more traditional day-to-day activities because: A) it has limited time frame. B) it has an unlimited budget. C) it is more expensive. D) it involves more of the workforce. Answer: A Diff: 2 Page Ref: 347 Section Heading: The Elements of Project Management Keywords: project management AACSB: Application of knowledge

78) A dummy activity is used to show a precedence relationship, but it does not represent a: A) relationship between activities. B) change in relationship. C) real activity. D) passage of time. Answer: D Diff: 2 Page Ref: 350 Section Heading: CPM/Pert Keywords: project network, dummy activities AACSB: Application of knowledge

20 .

79) The critical path is the ________ path through the network. A) longest B) shortest C) straightest D) most expensive Answer: A Diff: 2 Page Ref: 352 Section Heading: CPM/Pert Keywords: project network, critical path AACSB: Application of knowledge

80) The advantage of a Gantt chart over other charts is its: A) feasibility. B) practicality. C) simplicity. D) linearity. Answer: C Diff: 3 Page Ref: 353 Section Heading: The Elements of Project Management Keywords: Gantt chart AACSB: Application of knowledge

81) In a CPM/PERT network the critical path is the: A) lowest path through the network. B) highest path through the network. C) shortest path through the network. D) longest path through the network. Answer: D Diff: 2 Page Ref: 352 Section Heading: CPM/Pert Keywords: project network AACSB: Application of knowledge

82) A Gantt chart represents mainly: A) an immediate identification of predecessor task. B) a record-keeping device used in scheduling activities. C) a general identifier. D) the number of workers directly involved in the project. Answer: B Diff: 2 Page Ref: 353 Section Heading: The Elements of Project Management Keywords: Gantt chart AACSB: Application of knowledge

21 .

83) If t is the expected completion time for a given activity, then: A) LF = LS - t. B) EF = ES - t. C) EF = ES + t. D) EF = LS - t. Answer: C Diff: 2 Page Ref: 354 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

84) The LS and LF are calculated using the: A) backward pass through the network. B) forward pass through the network. C) values for ES and EF. D) backward and forward pass through the network. Answer: A Diff: 2 Page Ref: 355 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

Consider the following project.

Activity A B C D E F G H

Immediate Processor A, B B C C, D D E, F, G

Activity Time (days) 6 8 5 4 7 3 6 5

85) Determine the critical path. A) ACEH B) BCEH C) BDFH D) BDGH Answer: B Diff: 2 Page Ref: 352 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

22 .

86) Determine the estimated completion time of the project. A) 23 days B) 22 days C) 25 days D) 20 days Answer: C Diff: 2 Page Ref: 352 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

87) Determine the slack for activity D. A) 2 days B) 4 days C) 6 days D) 5 days Answer: A Diff: 2 Page Ref: 356 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

88) Determine the slack for activity F. A) 2 days B) 3 days C) 4 days D) 5 days Answer: C Diff: 2 Page Ref: 356 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

89) How much can activity F be delayed without delaying the project completion? A) 1 day B) 2 days C) 3 days D) 4 days Answer: D Diff: 2 Page Ref: 356 Section Heading: CPM/Pert Keywords: PERT/CPM solution AACSB: Analytical thinking

23 .

90) A dummy activity in a PERT network allows us to: A) specify the positive time and resources required to complete the activity. B) maintain the precedence relationships. C) add more starting nodes. D) add more ending nodes. Answer: B Diff: 2 Page Ref: 350 Section Heading: CPM/Pert Keywords: project network diagram AACSB: Application of knowledge

Dinnertime A professor is planning an informal gathering for 100 or so of his closest friends. The project breaks down as follows: Activity Call planner Book caterer Hire quartet Schedule cleaning crew Stock wine cellar Hire valets Schedule butler overtime

Time 12 10 9 15 7 8 13

Predecessor Call planner Call planner Book caterer Schedule cleaning crew, Stock wine cellar Hire quartet, Hire valets

91) Which of these is not a critical path activity? A) hire quartet B) hire valets C) schedule butler D) schedule cleaning crew Answer: A Diff: 2 Page Ref: 359 Section Heading: The Elements of Project Management Keywords: project network, critical path activities AACSB: Analytical thinking

92) What is the slack time for the Stock wine cellar activity? A) 8 B) 10 C) 12 D) 14 Answer: B Diff: 2 Page Ref: 363 Section Heading: The Elements of Project Management Keywords: slack AACSB: Analytical thinking

24 .

93) What is the fastest this project can be completed? A) 34 B) 38 C) 44 D) 48 Answer: D Diff: 2 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

94) What is the early start time for the Hire valets activity? A) 31 B) 27 C) 23 D) 20 Answer: B Diff: 2 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

95) What is the late start time for the Stock wine cellar activity? A) 12 B) 17 C) 20 D) 24 Answer: C Diff: 2 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

96) Which activity has a slack time that is different from all others? A) hire quartet B) hire valets C) schedule butler D) schedule cleaning crew Answer: A Diff: 2 Page Ref: 363 Section Heading: The Elements of Project Management Keywords: slack AACSB: Analytical thinking

25 .

Predecessor A A B B D,E F C G,H,J

Duration

Early Start

Early Finish 10 7

Late Start

15 11

Late Finish 11

7 19

10 24 24 28 36

97) What is the early finish time for activity K? A) 36 B) 35 C) 34 D) 33 Answer: A Diff: 1 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

98) What is the late finish time for activity A? A) 9 B) 10 C) 11 D) 12 Answer: B Diff: 1 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

26 .

99) What is the slack time for activity C? A) 3 B) 2 C) 1 D) 0 Answer: D Diff: 1 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

100) What is the early start time for activity G? A) 11 B) 13 C) 15 D) 19 Answer: C Diff: 2 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

101) What is the late start time for activity H? A) 21 B) 24 C) 17 D) 23 Answer: A Diff: 2 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

102) What is the slack time for activity H? A) 1 B) 2 C) 3 D) 4 Answer: D Diff: 2 Page Ref: 361-362 Section Heading: The Elements of Project Management Keywords: early start, late start, early finish, late finish AACSB: Analytical thinking

27 .

103) Joe used a project management software package and has determined the following results for a given project: Expected completion time of the project = 22 days Variance of project completion time = 2.77 What is the probability of completing the project over 20 days? A) 0.3849 B) 0.8849 C) 0.1151 D) 0.7642 Answer: B Diff: 3 Page Ref: 370 Section Heading: Probabilistic Activity Times Keywords: probabilistic activity times, project duration AACSB: Analytical thinking

104) Joe used a project management software package and has determined the following results for a given project: Expected completion time of the project = 22 days Variance of project completion time = 2.77 What is the probability of completing the project within 20 days? A) 0.3849 B) 0.8849 C) 0.1151 D) 0.7642 Answer: C Diff: 2 Page Ref: 370 Section Heading: Probabilistic Activity Times Keywords: probabilistic activity times, project duration AACSB: Analytical thinking

105) A PERT/CPM activity has an optimistic time estimate of 3 days, a most likely time estimate of 8 days, and a pessimistic time estimate of 10 days. The expected time (in days) of this activity is: A) 7.0. B) 7.5. C) 8.0. D) 8.5. Answer: B Diff: 2 Page Ref: 370 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM AACSB: Analytical thinking

28 .

Thai Construction A construction firm from the Phuket Province of Thailand has a five activity project lined up for the coming month. They have had some difficulty getting firm estimates on the activity durations and have resorted to the three time estimates approach to plan the project. The activities and optimistic, most likely, and pessimistic estimates (in days) for each are shown in the table. Activity A B C D E

Predecessor A D

Optimistic 5 11 8 9 6

Most Likely 7 15 12 11 8

106) What is the expected time for activity B? A) 14.83 B) 15.00 C) 14.67 D) 14.33 Answer: A Diff: 2 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

107) What is the expected completion time for the project? A) 14.83 B) 16.67 C) 18.83 D) 19.00 Answer: D Diff: 2 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

108) What is the standard deviation of the AC path? A) 1.83 B) 1.67 C) 1.43 D) 2.00 Answer: C Diff: 2 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

29 .

Pessimistic 10 18 15 12 10

109) What is the likelihood that the B path is completed in under 15 days? A) 0.56 B) 0.27 C) 0.43 D) 0.16 Answer: A Diff: 2 Page Ref: 370 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

110) What is the likelihood that the project takes longer than 21 days to complete? A) 0.83 B) 0.24 C) 0.43 D) 0.16 Answer: B Diff: 2 Page Ref: 370 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

111) What deadline is equally likely for path DE and path AC? A) 18.6 days B) 17.4 days C) 16.2 days D) 15.0 days Answer: A Diff: 3 Page Ref: 370 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM solution, probabilistic analysis AACSB: Analytical thinking

112) A PERT/CPM activity has an optimistic time estimate of 3 days, a most likely time estimate of 8 days, and a pessimistic time estimate of 10 days. The standard deviation of this activity is: A) 7/9. B) 7/6. C) 1/3. D) 2/3. Answer: B Diff: 1 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM AACSB: Analytical thinking

30 .

113) A PERT/CPM activity has an optimistic time estimate of 4 days, a most likely time estimate of 6 days, and a pessimistic time estimate of 10 days. The expected time (in days) of this activity is: A) 6.0. B) 6.33. C) 7.0. D) 7.5. Answer: B Diff: 2 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM AACSB: Analytical thinking

114) A PERT/CPM activity has an optimistic time estimate of 4 days, a most likely time estimate of 6 days, and a pessimistic time estimate of 10 days. The standard deviation of this activity is: A) 7/6. B) 1/3. C) 2/3. D) 1.0. Answer: D Diff: 1 Page Ref: 367 Section Heading: Probabilistic Activity Times Keywords: PERT/CPM AACSB: Analytical thinking

115) The normal cost for an activity is $7,000 and the crash cost is $12,000. The normal time to complete this activity is 8 days and crash time is 4 days. If this activity is crashed by 2 days it will cost an additional: A) $1000 B) $1250 C) $2000 D) $2500 Answer: D Diff: 2 Page Ref: 377 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: time-cost trade off AACSB: Analytical thinking

116) Which of these statements regarding project crashing is true? A) Crashing is not possible unless there are multiple critical paths. B) Activities not on the critical path cannot become critical after crashing. C) Crashing shortens the project duration by assigning more resources to one or more of the critical tasks. D) Crashing a project often reduces the time it takes for lengthy or complex, but noncritical activities. Answer: C Diff: 1 Page Ref: 376 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: PERT/CPM AACSB: Analytical thinking

31 .

The diagram below shows the activities on the nodes, and the table shows the normal time and crash time (in days) and cost for each activity.

Activity

Normal Time

Crash Time

A B C D E F

6 10 5 4 9 2

6 8 4 1 7 1

Cost per day to crash --$100 $300 $700 $500 $650

117) Which activity should be crashed to reduce the project completion time by one day? A) E B) B C) C D) D Answer: C Diff: 1 Page Ref: 377 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: crashing, time-cost tradeoffs AACSB: Analytical thinking

118) Which activity should be crashed to reduce the project completion by 2 days? A) Crash activity B by 1 day and Activity C by 1 day. B) Crash activity E by 2 days. C) Crash activity C by 1 day and activity E by 1 day. D) Crash activity B by 2 days. Answer: C Diff: 1 Page Ref: 377 Section Heading: Project Crashing and Time-Cost Trade-Off Keywords: crashing, time-cost tradeoffs AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 9 Multicriteria Decision Making 1) The different objectives in a goal programming problem are referred to as goals. Answer: TRUE Diff: 1 Page Ref: 417 Section Heading: Goal Programming Keywords: goal programming AACSB: Application of knowledge

2) A negative deviational variable is the amount by which a goal level is exceeded. Answer: FALSE Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: goal constraints, deviational variable AACSB: Application of knowledge

3) At least one or both deviational variables in a goal constraint must equal 0. Answer: TRUE Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variable, goal constraints AACSB: Application of knowledge

4) The objective function in a goal programming model seeks to minimize the deviation from goals in the order of the goal priorities. Answer: TRUE Diff: 2 Page Ref: 418 Section Heading: Goal Programming Keywords: goal prog problem formulation, objective function for goal prog AACSB: Application of knowledge

5) In goal programming, terms are summed in the objective function in order to make consistent decisions. Answer: FALSE Diff: 2 Page Ref: 419 Section Heading: Goal Programming Keywords: goal prog problem formulation, objective function for goal prog AACSB: Application of knowledge

6) Goal constraints can include all deviational variables. Answer: TRUE Diff: 1 Page Ref: 419 Section Heading: Goal Programming Keywords: deviational variable, goal constraints AACSB: Application of knowledge

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7) In goal programming, problems cannot have two or more goals at the same priority level. Answer: FALSE Diff: 1 Page Ref: 420 Section Heading: Goal Programming Keywords: goal prog problem formulation, objective function for goal prog AACSB: Application of knowledge

8) Goal programming provides a method for simultaneously striving to achieve several objectives. Answer: TRUE Diff: 2 Page Ref: 416 Section Heading: Goal Programming Keywords: goal prog problem formulation, objective function for goal prog AACSB: Application of knowledge

9) One goal is never achieved at the expense of another higher-priority goal. Answer: TRUE Diff: 1 Page Ref: 421 Section Heading: Graphical Interpretation of Goal Programming Keywords: graphical solution to a goal prog problem, goal achievement AACSB: Application of knowledge

10) A goal can be achieved at the expense of another lower-priority goal. Answer: TRUE Diff: 1 Page Ref: 421 Section Heading: Graphical Interpretation of Goal Programming Keywords: graphical solution to a goal prog problem, goal achievement AACSB: Application of knowledge

11) In a goal programming model, the terms in the objective function are summed to determine the maximum profit or minimum cost. Answer: FALSE Diff: 1 Page Ref: 419 Section Heading: Goal Programming Keywords: goal prog model, objective function of the goal prog model AACSB: Application of knowledge

12) Objective function terms are not summed in goal programming because not all goals are achievable. Answer: FALSE Diff: 1 Page Ref: 419 Section Heading: Goal Programming Keywords: goal programming AACSB: Application of knowledge

13) Goal programming violates the divisibility property of linear programming. Answer: FALSE Diff: 1 Page Ref: 416 Section Heading: Graphical Interpretation of Goal Programming Keywords: goal programming AACSB: Application of knowledge

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14) In a pairwise comparison, two alternatives are compared according to a criterion and one is preferred. Answer: TRUE Diff: 1 Page Ref: 431 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process, pairwise comparison AACSB: Application of knowledge

15) A preference scale assigns numerical values to different levels of preference. Answer: TRUE Diff: 2 Page Ref: 431 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process, preference scale AACSB: Application of knowledge

16) On a preference scale for pairwise comparisons, the number "1" indicates that two objects are equally preferred. Answer: TRUE Diff: 2 Page Ref: 431 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process, pairwise comps, preference scale AACSB: Application of knowledge

17) In synthesization, decision alternatives are prioritized within each criterion. Answer: TRUE Diff: 2 Page Ref: 432 Section Heading: The Analytical Hierarchy Process Keywords: synthesization AACSB: Application of knowledge

18) A consistency index measures the degree of inconsistency in pairwise comparisons. Answer: TRUE Diff: 1 Page Ref: 436 Section Heading: The Analytical Hierarchy Process Keywords: consistency index AACSB: Analytical thinking

19) A preference scale assigns numerical values to different levels of preferences. Answer: TRUE Diff: 2 Page Ref: 436 Section Heading: The Analytical Hierarchy Process Keywords: preference scale AACSB: Application of knowledge

20) In a given AHP problem, the consistency index is .15, and the random index is .90. In this instance, there are probably serious inconsistencies and, therefore, the AHP result may not be meaningful. Answer: TRUE Diff: 2 Page Ref: 436 Section Heading: The Analytical Hierarchy Process Keywords: consistency index AACSB: Application of knowledge

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21) Scoring models use consistency indexes to measure the degree of consistency between choices. Answer: FALSE Diff: 1 Page Ref: 440 Section Heading: Scoring Models Keywords: scoring AACSB: Application of knowledge

22) In scoring models, the two alternatives with the highest scores are compared to make the final decision. Answer: FALSE Diff: 1 Page Ref: 433 Section Heading: Scoring Models Keywords: scoring AACSB: Application of knowledge

23) At least one or both deviational variables in a goal constraint must equal ________. Answer: zero Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables, goal constraints AACSB: Application of knowledge

24) Consider the following constraint: 2x1 + 3x2 = 60. Assume that we convert this constraint into a goal constraint with the value of x1 = 15 and the value of x2 = 15. Then the values of d1+ and d1- are ________ and ________, respectively. Answer: 15; 0 Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables, goal constraints AACSB: Analytical thinking

25) A(n) ________ variable is the amount by which a goal level is underachieved. Answer: negative deviational Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables AACSB: Application of knowledge

26) A(n) ________ variable is the amount by which a goal level is exceeded. Answer: positive deviational Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables AACSB: Application of knowledge

27) A(n) ________ assigns numerical values to different levels of preferences. Answer: preference scale Diff: 2 Page Ref: 423 Section Heading: Analytical Hierarchy Process Keywords: preference scale AACSB: Application of knowledge

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28) A(n) ________ measures the degree of inconsistency in pairwise comparisons. Answer: consistency index Diff: 2 Page Ref: 429 Section Heading: Analytical Hierarchy Process Keywords: consistency index AACSB: Application of knowledge

29) A ________ vector is the average of the values in each row of the normalized matrix in the AHP process. Answer: preference Diff: 1 Page Ref: 425 Section Heading: Analytical Hierarchy Process Keywords: preference vector, AHP AACSB: Application of knowledge

30) If the CI/RI ratio is more than ________, then there are probably serious inconsistencies in the AHP results. Answer: .10 Diff: 2 Page Ref: 431 Section Heading: Analytical Hierarchy Process Keywords: consistency, AHP AACSB: Analytical thinking

31) The analytic hierarchy process, scoring models, and goal programming are all considered to be ________ decision making techniques because they incorporate decisions based on more than one objective. Answer: multiple criteria Diff: 2 Page Ref: 416 Section Heading: Goal Programming Keywords: multiple criteria decision making AACSB: Application of knowledge

32) In a facility location problem, if location A receives a score of 45 for the criteria "traffic congestion", which has a weight of .30; a score of 50 for the criteria "labor force", which has a weight of .45; and a score of 60 for "utilities", which has a weight of .25, the overall score for location A is ________. Answer: 51 Diff: 2 Page Ref: 433 Section Heading: Scoring Models Keywords: scoring AACSB: Analytical thinking

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33) The objective function formulation for a goal programming model is as follows: Min P1d1-, P2d2-, P3d1+, P4d3Which one of the variables would the program designers like to have as the second goal such that its deviation from zero is minimized? Answer: d2Diff: 1 Page Ref: 418 Section Heading: Goal Programming Keywords: goal prog formulation, objective function for a goal prog problem AACSB: Analytical thinking

34) The objective function formulation for a goal programming model is as follows: Min P1d1-, P2d2-, (4P4d3- + 6P4d2+) At the priority level 4, which one of the deviational variables is most important? Answer: d2+ Diff: 1 Page Ref: 418 Section Heading: Goal Programming Keywords: goal prog formulation, objective function for a goal prog problem AACSB: Analytical thinking

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Billy Hill's Still William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the hills of Kentucky. He makes two products, known among his customers as Rotgut and White Lightning. The recipes for the two have been passed down in the Hill family for generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which sell for $8 apiece for Rotgut and $12 apiece for White Lightning. A quick inventory one crisp autumn morning reveals that William has on hand 40 bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few artisnal batches, but has recently received a tip that certain agencies have taken an interest in his talents and may be paying him a visit in three days, hence he plans to restrict any brewing activity to 72 hours at most, before he retreats to his home away from home, Lubbock. William cleans his equipment, lights a fire, and ponders the objectives. Obviously the first priority is restricting himself to 72 hours of work — any more than that and he runs the risk of an extended holiday. His second priority to make enough to acquire materials for the next production run and fund his daughter's college tuition - he believes that $500 would make this production run worth his while. His third and fourth priorities are not to have too much perishable inventory, so he wants to make sure he doesn't have too many bushels of corn on hand (third priority) nor does he want too many pounds of sugar on hand (fourth priority). 35) What is the objective function? Answer: Minimize P1d1+,P2d2-,P3d3+,P4d4+ Diff: 3 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

36) What is the objective function? Answer: Minimize P1d1+,P2d2-,P3d3+,P4d4+ Diff: 3 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

37) What is the time constraint? Answer: 2R + 3W + d1+ + d1- = 72 Diff: 2 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

38) What is the sugar constraint? Answer: 3R + 2W + d4+ + d4- = 70 Diff: 2 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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39) What is the corn constraint? Answer: 3R + 2W + d3+ + d3- = 40 Diff: 2 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

40) What is the profit constraint? Answer: 16R + 24W + d2+ + d2- = 500 Diff: 2 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

41) Formulate the goal programming model. Answer: Minimize P1d1+,P2d2--,P3d3+,P4d4+ 2R + 3W + d1+ + d1- = 72 16R + 24W + d2+ + d2- = 500 3R + 2W + d3+ + d3- = 40 3R + 2W + d4+ + d4- = 70 Diff: 3 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

42) This model was run in Excel and a portion of the answer report appears below. Provide an interpretation that includes the revenue realized from the production run. Variable Cells Cell

Name

$C$14 White Lightning $D$16 Hours d1+ $E$16 Hours d1-

Original Value

Final Value

Integer

0 0 0

12.5 0 9.5

Contin Contin Contin

Answer: There are 12.5 batches of Rotgut and 12.5 batches of White Lightning being produced with a usage of hours that is 9.5 hours fewer than the limit of 72 hours. At 12.5 batches of each blend, the income is 12.5 × $24 + 12.5 × $16 = $500 Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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43) This model was run in Excel and a portion of the answer report appears below. Provide an interpretation. Variable Cells Cell

Name

Original Value

Final Value

Integer

$D$19 $E$19

Sugar d4+ Sugar d1-

0 0

7.5 0

Contin Contin

Answer: The d3+ variable has a value of 2.5, meaning that the amount of corn needed was 2.5 bushels less than the maximum amount (40 bushels) that William wanted to carry. The value of d4+ is 7.5, so the amount of sugar needed was 7.5 pounds less than the maximum (70 pounds) William wanted to have on hand. Thus, William needed only 37.5 bushels of corn and 62.5 pounds of sugar. Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

44) William ran the original model in Excel and discovered that he was walking away from significant income. He reformulated the model with a new profit constraint of 16R + 24W + d 2+ + d2- = 550. All of the other constraints and priorities remained the same. Based on this snippet of the sensitivity report, what should happen during this production run? Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$14 Rotgut 10 0 0 0 0 $C$14 White Lightning 15 0 0 0 0 $D$16 Hours d1+ 0 1 1 1E+30 1 $E$16 Hours d17 0 0 1 0 $D$17 Profit d2+ 30 0 0 0 0 $E$17 Profit d20 0 0 1E+30 0 Answer: William should produce 10 batches of Rotgut and 15 batches of white lightning. The d2+ variable is 30, so the secondary objective of $550 profit will fall short by $30. This could also be confirmed simply by $24 × 15 + $16 × 10 = $520. The d1- variable is 7, meaning that the required time of 65 hours falls short of the 72 hours William thought he had available. This should give him plenty of time to hide the ten pounds of sugar that he has left over, load up The General, and drive to Lubbock. Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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45) William ran the original model in Excel and discovered that he was walking away from significant income. He reformulated the model with a new profit constraint of 16R + 24W + d 2+ + d2- = 550. All of the other constraints and priorities remained the same. Based on this snippet of the answer report, what happens during this production run?

$D$16 $E$16 $D$17 $E$17 $D$18 $E$18 $D$19 $E$19

Variable Cells Hours d1+ Hours d1Profit d2+ Profit d2Corn d3+ Corn d3Sugar d4+ Sugar d4-

0 0 0 0 0 0 0 0

0 7 30 0 0 0 0 10

Contin Contin Contin Contin Contin Contin Contin Contin

Answer: William will be producing such that he has 7 hours to work with, that is he is using 7 hours fewer than his 72 hour maximum. The mix he is producing results in falling short of his $550 hoped-for income by $30. William has 10 pounds of sugar left over from the 70 pounds he started the production run with. William is using all the corn he had on hand — all 40 bushels. Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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Ashley's manufactures home furnishings for department stores. Planning is underway for the production of the following items during the next production period: Quilts (x1)

Blinds (x2)

Pillows (x3)

Fabric required (yards) (d1)

Time required (hours) (d2)

1.5

0.5

Packaging material (ounces) (d3)

Profit (d4)

Ashley has 3000 yards of material in stock for this production period. Five hundred hours of production time are scheduled and 400 ounces of packaging material is available. Each of these quantities can be adjusted through overtime or extra purchases. Ashley's highest priority is to achieve a profit of $3200. Her second priority is to avoid additional purchases of packaging material. Third, she wants to use all of the scheduled production hours, and fourth, minimize any fabric remaining from the 3000 yards. Note that the deviational variables associated with each item are given in the table. 46) What is the objective function? Answer: Min P1d4-, P2d3+, P3d2-, P4d1+ Diff: 3 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal prog formulation, objective function for a goal prog problem AACSB: Analytical thinking

47) What is the fabric constraint? Answer: 7x1 + 4x2 + 9x3 + d1- - d1+ = 3000 Diff: 2 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal prog formulation, constraints for a goal prog problem AACSB: Analytical thinking

48) What is the profit constraint? Answer: 12x1 + 10x2 + 8x3 + d4- - d4+ = 3200 Diff: 2 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal prog formulation, constraints for a goal prog problem AACSB: Analytical thinking

49) What is the production time constraint? Answer: 1.5x1 + 2x2 + 0.5x3 + d2- - d2+ = 500 Diff: 2 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal prog formulation, objective function for a goal prog problem AACSB: Analytical thinking

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50) What is the packaging material constraint? Answer: 3x1 + 2x2 + 1x3 + d3- - d3+ = 400 Diff: 2 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal prog formulation, constraints for a goal prog problem AACSB: Analytical thinking

An investor has $80,000 to invest in three stocks, stock A costs $100, stock B costs $120 and stock C costs $80. Each stock A has a risk factor of 8, each stock B has a risk factor of 10 and each stock C has a risk factor of 7. The investor believes that the sum of the risk factors for all stocks purchase should not exceed 6000. The projected annual growth rate for the three stocks are 9%, 13% and 8% respectively. The projected annual dividend income from these stocks are as follows: Stock A: $14/stock, Stock B: $15/stock, and Stock C: $20/stock. The investor desires an annual dividend income of $10,000. The investor has established the following goals in order of their importance: (1) The investor believes that the budget cannot be exceeded. (d1) (2) The risk factor should not exceed the target amount of 6000. (d2) (3) The average annual growth rate in stock prices must be at least 10%. (d3) (4) The investor desires a dividend income of at least $10,000. (d4) 51) State the goal programming objective function. Answer: Min P1d1+, P2d2+, P3d3-, P4d4Diff: 3 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal programming objective function AACSB: Analytical thinking

52) Write the budget constraint Answer: 100A + 120B + 80C + d1- - d1+ = 80,000 Diff: 2 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal programming constraints AACSB: Analytical thinking

53) Write the risk factor constraint Answer: 8A + 10B + 7C + d2- - d2+ = 6000 Diff: 2 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal programming constraints AACSB: Analytical thinking

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54) Centerville city council is in the process of developing city tax rates. The annual tax base for real estate property is $750 million and for general sales, $80 million. Annual local gas consumption is estimated at 12 million gallons. They have three goals, listed in order of priority: 1. Tax revenues must be at least $25 million to meet the city's financial commitments. 2. Sales tax cannot exceed 25% of all taxes collected. 3. Gasoline tax cannot exceed 8 cents per gallon. Formulate as a goal programming problem. Answer: Let xp = tax rate for property; xs = sales tax rate, and xg = gas tax in cents per gallon. Min P1d1-, P2d2-, P3d3+ Subject to: 750xp + 80xs + .12xg ≥ 25 80xs ≤ .25(750xp + 80xs + .12xg) xg ≤ 8 Simplify the second constraint: 187.5xp - 60xs +.03xg ≥ 0. If this constraint is written as -187.5xp + 60xs -.03xg = 0, then the objective function should be: Min P1d1-, P2d2+, P3d3+. Diff: 3 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal programming formulation AACSB: Analytical thinking

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A production of 300 units of Twiddle Bugs, an educational toy for children, must be completed within 1 week by BugU Manufacturing. Two production lines are available, each for 30 hours during the week. Production line 1 can produce five units per hour and production line 2 can produce four units an hour. Line 1 costs $50 per hour to operate and line 2 costs $55 per hour. Overtime is available for line 1 at $15 per hour and for line 2 at $12 per hour. Management goals in decreasing order are: P1: Produce 300 units. P2: Maximum allowable overtime of 6 hours for line 1. P3: Cost of overtime must not exceed $750. P4: Avoid the underutilization of either production line. Assign weights that are proportional to their production capability. P5: Producing more than 300 units is 1-1/2 times as undesirable as producing under 300 units. 55) What are the constraints for this problem? Answer: Let x1 = hours of production time on line 1. x2 = hours of production time on line 2. 5x1 + 4x2 = 300 x1≤ 30 x2 ≤ 30 P1: 5x1 + 4x2 + d1- - d1+ = 300 P2: x1 + d2- - d2+=36 P3: 50(x1 - 30) + 55(x2 - 30) + d2- - d2+ = 750 or 50x1 + 55x2 + d2- - d2+ = 3150 P4a: x1 + d4- - d4+=30 P4b: x2 + d5- - d5+=30 P5: See objective function. Objective function: Minimize P1Ad1- + 1.5 P1Bd1+ + P2d2+ + P3d3+ + 5P4Ad4- + 4P4Bd5Diff: 2 Page Ref: 416-419 Section Heading: Goal Programming Keywords: goal programming, constraints AACSB: Analytical thinking

56) What is the objective function? Answer: Minimize P1Ad1- + 1.5 P1Bd1+ + P2d2+ + P3d3+ + 5P4Ad4- + 4P4Bd5Diff: 2 Page Ref: 419 Section Heading: Goal Programming Keywords: goal programming, objective function AACSB: Analytical thinking

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57) Assume that a decision maker using analytical hierarchy process generated the following pairwise comparison matrix.

Calculate the normalized matrix. Answer: normalized matrix: Diff: 2 Page Ref: 433 Section Heading: The Analytical Hierarchy Process Keywords: pairwise comparison matrix, normalized matrix AACSB: Analytical thinking

58) Using the normalized matrix given below, calculate the row averages.

Answer: row average 1.00 Diff: 1 Page Ref: 433 Section Heading: The Analytical Hierarchy Process Keywords: normalized matrix, row average AACSB: Analytical thinking

59) Assume that a decision maker has to make a choice between three types of cars. Chevy, Honda, and Ford. Based on three criteria: comfort, MPG, and style. The row averages for criteria is summarized in the following column vector:

The preference matrix for the three types of cars is given as follows:

Compute the overall score for each decision alternative (car). Answer: Chevy = .29 Honda = .48 Ford = .23 Diff: 2 Page Ref: 434 Section Heading: The Analytical Hierarchy Process Keywords: AHP, overall score AACSB: Analytical thinking

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60) Assume that a plant manager has to decide where to locate its warehouse. The decision has been narrowed down to choices among the following three cities: Detroit, Cleveland, and St. Louis. The following pairwise comparison matrix summarizes the preferences of the plant manager. Cleveland 1/3 1 2

St. Louis 1/4 1/2 1

Determine the normalized matrix. Answer: Detroit Cleveland Detroit .125 .10 Cleveland .375 .30 St. Louis .500 .60

St. Louis .1429 .2857 .5714

Detroit Cleveland St. Louis

Detroit 1 3 4

Diff: 2 Page Ref: 433 Section Heading: The Analytical Hierarchy Process Keywords: pairwise comparison matrix, normalized matrix AACSB: Analytical thinking

61) Consider the following normalized matrix for car comfort that was computed using the analytical hierarchy process:

Car A Car B Car C

Car A 0.30 0.60 0.10

Car B 0.25 0.50 0.25

Car C 0.50 0.33 0.17

Which car is the most preferred based on comfort? Answer: Row averages indicate a preference for Car B. 0.35 0.48 0.17 Diff: 2 Page Ref: 433 Section Heading: The Analytical Hierarchy Process Keywords: preference vector AACSB: Analytical thinking

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62) The analytical hierarchy process was used to determine which car to purchase. Four criteria were used: price, miles per gallon, comfort, and durability. Consider the following normalized matrix and the preference vector for durability.

Multiplying the normalized matrix by the preference vector gives the following results: 2.17 2.26 1.69 Compute the consistency index. Answer: 2.17 0.36 = 5.958 2.26 0.59 = 3.797 1.69 0.41 = 4.092 sum = 13.847 avg of sum = 4.616 CI = 0.808 Very inconsistent! Diff: 3 Page Ref: 436-438 Section Heading: The Analytical Hierarchy Process Keywords: AHP, consistency AACSB: Analytical thinking

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63) Three job applicants were rated on four criteria, resulting in the following preference vectors: Applicant A B C

Criterion 1 .3085 .2147 .4768

Criterion 2 .0792 .4615 .4593

Criterion 3 .5986 .0126 .3888

The priorities of the criteria are: Criterion 1 2 3 4

Priority .2178 .1915 .4123 .1784

Rank the 3 applicants. Answer: Applicant Score A .4396 B .1947 C .3658 Applicant A is ranked highest and applicant B the lowest. Diff: 3 Page Ref: 435 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process solution method, calc of overall scores AACSB: Analytical thinking

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Criterion 4 .6192 .3045 .0763

64) Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Cleveland, and St. Louis. The company has weighted each of these criteria in terms of its relative importance in the decision making process, and it has analyzed each potential warehouse location and graded them according to each criteria as shown in the following table.

Decision Criteria

Weight

Proximity to suppliers Proximity to customers Land and construction costs

.45 .35 .20

Grades for Grades for Grades for Detroit Cleveland St. Louis 80 70 60 75 90 80 60 50 85

Calculate the scores for each location and state where the warehouse should be located. Answer: SDetroit = 74.25 SCleveland = 73 SSt.Louis = 72 Choose Detroit. Diff: 2 Page Ref: 433 Section Heading: Scoring Models Keywords: scoring model AACSB: Analytical thinking

65) A business is trying to decide which restaurant to hold its annual awards banquet. Use the information below to determine the best choice.

Criteria Appearance Service Atmosphere Location Quality of food

Weight 0.15 0.30 0.15 0.10 0.30

A 40 75 60 90 70

Restaurant B C 65 60 80 70 40 70 100 75 80 75

Answer: A score = 67.5, B score = 73.75, C score = 70.5. Select B. Diff: 2 Page Ref: 433 Section Heading: Scoring Models Keywords: scoring AACSB: Analytical thinking

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66) A positive deviational variable is the amount by which a goal level is: A) underachieved. B) exceeded. C) minimized. D) maximized. Answer: B Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables, goal constraints AACSB: Application of knowledge

67) A ________ deviational variable is the amount by which a goal level is exceeded. A) negative B) positive C) positive or negative D) positive and negative Answer: B Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables, goal constraints AACSB: Application of knowledge

68) At least one or both deviational variables in a goal constraint must equal: A) 1. B) -1. C) 0. D) 2. Answer: C Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables, goal constraints AACSB: Application of knowledge

69) A decision with more than one objective: A) should be decomposed into a separate model for each objective. B) depends on the probability of satisfying each objective. C) requires the decision maker to put the objectives in some order of importance. D) cannot have an optimal solution. Answer: C Diff: 1 Page Ref: 417 Section Heading: Goal Programming Keywords: objective function for a goal programming problem AACSB: Application of knowledge

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70) Deviation variables: A) represent the actual value of the function part of a goal constraint. B) represent the difference between the target and actual values. C) must sum to 1. D) equal the difference between actual and predicted values of the decision variables. Answer: B Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables, goal programming model AACSB: Application of knowledge

71) The objective function min P1d1- , P2d2+: A) attempts to avoid being below target for the priority 1 goal. B) attempts to avoid being below target for the priority 2 goal. C) will not have any feasible solutions. D) will have a solution only if P1 > P2. Answer: A Diff: 1 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

72) The majority of the goal constraints are equalities that include ________ variables. A) only deviational B) deviational and decision C) only decision D) neither deviational nor decision variables Answer: B Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Application of knowledge

73) A ________ deviational variable is the amount by which a goal level is underachieved. A) negative B) positive C) positive or negative D) positive and negative Answer: A Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Application of knowledge

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74) The objective function in a goal programming model seeks to ________ the deviation from goals in the order of the goal priorities. A) free B) even out C) maximize D) minimize Answer: D Diff: 2 Page Ref: 418 Section Heading: Goal Programming Keywords: goal prog formulation, objective function for a goal prog problem AACSB: Application of knowledge

75) Goal constraints can include ________ deviational variables. A) no B) some C) all D) multiple Answer: C Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Application of knowledge

76) Deviational variables in a goal programming model constraint represent the: A) underachievement or overachievement of a goal level. B) resource constraint as defined by the linear model. C) probability of an optimal solution. D) probabilistic variables in the objective constraints. Answer: A Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: deviational variables, goal programming formulation AACSB: Application of knowledge

77) Two or more goals at the same priority level can be assigned weights to indicate their relative: A) meaning. B) slack. C) difference. D) importance. Answer: D Diff: 2 Page Ref: 418 Section Heading: Goal Programming Keywords: goal programming solution AACSB: Application of knowledge

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Billy Hill's Still William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the hills of Kentucky. He makes two products, known among his customers as Rotgut and White Lightning. The recipes for the two have been passed down in the Hill family for generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which sell for $8 apiece for Rotgut and $12 apiece for White Lightning. A quick inventory one crisp autumn morning reveals that William has on hand 40 bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few artisnal batches, but has recently received a tip that certain agencies have taken an interest in his talents and may be paying him a visit in three days, hence he plans to restrict any brewing activity to 72 hours at most, before he retreats to his home away from home, Lubbock. William cleans his equipment, lights a fire, and ponders the objectives. Obviously the first priority is restricting himself to 72 hours of work — any more than that and he runs the risk of an extended holiday. His second priority to make enough to acquire materials for the next production run and fund his daughter's college tuition - he believes that $500 would make this production run worth his while. His third and fourth priorities are not to have too much perishable inventory, so he wants to make sure he doesn't have too many bushels of corn on hand (third priority) nor does he want too many pounds of sugar on hand (fourth priority). 78) Which is the appropriate objective function for this scenario? A) minimize P1d1+,P2d2--,P3d3+,P4d4+ B) maximize Z = $16R + $24W C) maximize Z = $8R + $12W D) maximize P1d1-,P2d2+-,P3d3-,P4d4Answer: A Diff: 2 Page Ref: 418-419 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

79) Which is the appropriate profit constraint for this scenario? A) 16R + 24W + 16d2+ + 24d2- = 500 B) 16R + 24W + d2+ + d2- = 500 C) 16R + 24W + 16d2+ + 16d2- + 24d2+ + 24d2-= 500 D) 16R + 24W + 16d2+ + 24d2- ≥ 500 Answer: B Diff: 2 Page Ref: 418-419 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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80) Which is the appropriate time constraint for this scenario? A) 2R + 3W + d2+ + d2- = 72 B) 2R + 3W + d1+ + d1- ≤ 72 C) 2R + 3W + d1+ + d1- = 72 D) 2R + 3W + d2+ + d2- ≤ 72 Answer: C Diff: 2 Page Ref: 418-419 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

81) Which is the appropriate corn constraint for this scenario? A) 3R + 2W + d3+ + d3- ≤ 40 B) 3R + 2W + d3+ + d3- ≥ 40 C) 3R + 2W + 3d3+ + 2d3- ≤ 40 D) 3R + 2W + d3+ + d3- = 40 Answer: D Diff: 2 Page Ref: 418-419 Section Heading: Goal Programming Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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82) William ran the model in Excel and received both an answer and sensitivity report. Which of these statements about this portion of the sensitivity report is best? Variable Cells Cell

Name

$B$14 Rotgut $C$14 White Lightning $D$16 Hours d1+ $E$16 Hours d1$D$17 Profit d2+ $E$17 Profit d2$D$18 Corn d3+ $E$18 Corn d3$D$19 Sugar d4+ $E$19 Sugar d4-

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 12.5 12.5 0 9.5 0 0 2.5 0 7.5 0

0 0 1 0 0 0 0 0 0 0

0 0 1E+30 1 1E+30 1E+30 0 1E+30 0 1E+30

0 0 1 0 0 0 0 0 0

A) William needs only 62.5 hours to produce. B) William needs to acquire 2.5 additional bushels of corn. C) William needs 7.5 pounds more sugar. D) William needs 1 more hour to produce. Answer: A Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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83) William ran the model in Excel and received both an answer and sensitivity report. Which of these statements about this portion of the sensitivity report is best? Variable Cells Cell

Name

$D$16 $E$16 $D$17 $E$17 $D$18 $E$18 $D$19 $E$19

Hours d1+ Hours d1Profit d2+ Profit d2Corn d3+ Corn d3Sugar d4+ Sugar d4-

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease

0 9.5 0 0 2.5 0 7.5 0

1 0 0 0 0 0 0 0

1E+30 1 1E+30 1E+30 0 1E+30 0 1E+30

1 0 0 0 0 0 0

A) William needs 73 hours to produce. B) William will receive $500 of income from this run. C) William requires 7.5 additional pounds of sugar. D) William needs 1 more hour to produce. Answer: B Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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84) William ran the model in Excel and received both an answer and sensitivity report. Which of these statements about this portion of the sensitivity report is best? Variable Cells Cell

Name

$D$16 $E$16 $D$17 $E$17 $D$18 $E$18 $D$19 $E$19

Hours d1+ Hours d1Profit d2+ Profit d2Corn d3+ Corn d3Sugar d4+ Sugar d4-

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease

0 9.5 0 0 2.5 0 7.5 0

1 0 0 0 0 0 0 0

1E+30 1 1E+30 1E+30 0 1E+30 0 1E+30

1 0 0 0 0 0 0

A) William needs 73 hours to produce. B) William needs 2.5 additional bushels of corn. C) William has 7.5 pounds of sugar more than he needs. D) William needs 1 more hour to produce. Answer: C Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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85) William ran the model in Excel and received both an answer and sensitivity report. Which of these statements about this portion of the sensitivity report is best? Variable Cells Cell

Name

$D$16 $E$16 $D$17 $E$17 $D$18 $E$18 $D$19 $E$19

Hours d1+ Hours d1Profit d2+ Profit d2Corn d3+ Corn d3Sugar d4+ Sugar d4-

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease

0 9.5 0 0 2.5 0 7.5 0

1 0 0 0 0 0 0 0

1E+30 1 1E+30 1E+30 0 1E+30 0 1E+30

1 0 0 0 0 0 0

A) William needs 73 hours to produce. B) William income cannot be determined from this report. C) William has 7.5 pounds of sugar more than he needs. D) William has 2.5 bushels of corn left over. Answer: D Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

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86) William realizes he wasn't as ambitious as he should have been, and decides to reformulate his model such that the second priority is income of $550. After pressing "Solve" he reviews the sensitivity report shown below. Which statement is best? Variable Cells Cell

Name

$B$14 Rotgut $C$14 White Lightning $D$16 Hours d1+ $E$16 Hours d1$D$17 Profit d2+ $E$17 Profit d2$D$18 Corn d3+ $E$18 Corn d3$D$19 Sugar d4+ $E$19 Sugar d4-

Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 10 15 0 7 30 0 0 0 0 10

0 0 1 0 0 0 0 0 0 0

0 0 1E+30 1 0 1E+30 1E+30 1E+30 1E+30 0

0 0 1 0 0 0 0 0 0 0

A) William income has increased from $500 to $520. B) William income cannot be determined from this report. C) William can increase his profit beyond $550 is he would revise his profit constraint again. D) William's income has increased from $500 to $530. Answer: A Diff: 2 Page Ref: 425-429 Section Heading: Computer Solution of Goal Programming Problems with QM for Windows and Excel Keywords: goal programming formulation, goal constraints AACSB: Analytical thinking

87) A company has three goals, listed in order of importance. 1. Achieve a total profit of at least $240 million. 2. Maintain the current employment level of 3,000 employees 3. Invest no more than $70 million in capital. What is the objective function for a goal program for this situation? A) Min P1d1- , P2d2- , P3d3+ B) Min P1d1- , P2d2+ , P2d2- , P3d3C) Min P1d1- , P2d2- , P2d2- , P3d3+ D) Min P1d1+ , P2d2- , P2d2- , P3d3+ Answer: C Diff: 2 Page Ref: 417-418 Section Heading: Goal Programming Keywords: goal programming, objective function AACSB: Analytical thinking

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88) If the constraint 3x1 + 4x2 + (d1-) - (d1+) = 250 measures hours, then: A) 3x1 + 4x2 is equal to the actual time spent. B) if d1- is equal to 25, then 3x1 + 4x2 must equal 25. C) overtime could be represented by d1-. D) hours can take only an integer value. Answer: A Diff: 2 Page Ref: 418-419 Section Heading: Goal Programming Keywords: goal programming constraints AACSB: Analytical thinking

89) A company has a goal to maintain the current employment level, but places more importance on laying employees off than on hiring new employees. In other words, the company would rather hire than lay off employees. If the company assigns a "penalty weight" of 4 for the amount under the employment goal (goal 2) and a weight of 2 for the amount over the employment goal, how would this be expressed in the objective function? A) Min 4P2d2- + 2P2d2+ B) Min 2P2d2- + 4P2d2+ C) Max 4P2d2- + 2P2d2+ D) Min 4P2d2+ + 2P2d2Answer: A Diff: 2 Page Ref: 417-418 Section Heading: Goal Programming Keywords: goal programming, objective function AACSB: Analytical thinking

90) A company has a goal of calling on at least 400 customers a month (goal 1), but no fewer than 260 customers a month (goal 2). If X represents the number of customers contacted, which pair of constraints listed below is the appropriate representation in a goal programming problem? A) X + d1- - d1+ = 400, X + d2- - d2+ = 260 B) X - d1- + d1+ = 400, X - d2- - d2+ = 260 C) X - d1- + d1+ = 400, X + d2- - d2+ = 260 D) X + d1- - d1+ = 400, X - d2- + d2+ = 260 Answer: A Diff: 2 Page Ref: 417-418 Section Heading: Goal Programming Keywords: goal programming, constraints AACSB: Analytical thinking

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91) Consider the following constraint: 2x1 + 3x2 =60. Assume that we convert this constraint into a goal constraint with the value of x1 = 15 and the value of x2 = 15. Then the values of d1+ and d1- are ________ and ________, respectively. A) 0, 15 B) 15, 0 C) 20, 0 D) 0, 20 Answer: B Diff: 2 Page Ref: 417 Section Heading: Goal Programming Keywords: goal programming solution AACSB: Analytical thinking

92) The objective function in all goal programming models is to ________ from the goal constraint levels. A) maximize alternatives B) minimize alternatives C) minimize deviation D) maximize deviation Answer: C Diff: 3 Page Ref: 418 Section Heading: Goal Programming Keywords: objective function of a goal programming problem AACSB: Application of knowledge

Riverside Industries makes two products and each product is processed in three departments. The time requirements for each product in each department are given below. The profit for each product is also provided as well as the available hours in each department. Product Department A 1 3 2 2 Available Hours 600

Department B 4 1 400

Department C 2 2 400

Profit 1 2

Management wants to achieve three goals. The first two goals are equal in priority. Priority 1: Produce at least 125 units of product 1. Priority 1: Produce at least 80 units of product 2. Priority 2: Achieve a profit of at least 300. 93) The goal programming model for this problem has how many constraints? A) 3 B) 4 C) 6 D) 7 Answer: C Diff: 1 Page Ref: 417-418 Section Heading: Goal Programming Keywords: goal constraints AACSB: Analytical thinking

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94) The goal programming constraint for the first goal is: A) 3x1 + d1- - d1+ = 125. B) 3x1 - d1- + d1+ = 125. C) 1x1 + d1- - d1+ = 125. D) 1x1 - d1- + d1+ = 125. Answer: C Diff: 1 Page Ref: 417-418 Section Heading: Goal Programming Keywords: goal constraints AACSB: Analytical thinking

95) The objective function for this goal program is: A) Min P1d1- + P1d2-, P2d3-. B) Min P1d1+ + P1d2-,P2d3-. C) Min P1d1- + P1d2+, P2d33-. D) Min P1d1- + P1d2-, P2d3+. Answer: A Diff: 1 Page Ref: 418 Section Heading: Goal Programming Keywords: goal constraints AACSB: Analytical thinking

96) If the second goal was to produce no more than 80 units of product two, the objective function would be: A) Min P1d1- + P1d2-, P2d3-. B) Min P1d1+ + P1d2-, P2d3-. C) Min P1d1- + P1d2+, P2d3-. D) Min P1d1- + P1d2-, P2d3+. Answer: C Diff: 1 Page Ref: 418 Section Heading: Goal Programming Keywords: goal constraints AACSB: Analytical thinking

97) Goal programming solutions achieve the ________ satisfactory solution possible. A) best or most B) worst or least C) only D) somewhat Answer: A Diff: 2 Page Ref: 423 Section Heading: Goal Programming Keywords: graphical solution to a goal programming problem AACSB: Application of knowledge

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98) If choice A is strongly preferred to choice B and choice B is moderately preferred to choice C, and the decision maker says choice C is equally preferred to choice A, what conclusion can be drawn? A) The decision maker is consistent. B) The decision maker is inconsistent. C) The pairwise comparison matrix is symmetric. D) The decision maker has already synthesized. Answer: B Diff: 1 Page Ref: 424 Section Heading: Analytical Hierarchy Process Keywords: synthesization AACSB: Application of knowledge

99) In synthesization, decision alternatives are prioritized ________ criteria/ion. A) within some B) among some C) among all D) within each Answer: D Diff: 2 Page Ref: 432 Section Heading: The Analytical Hierarchy Process Keywords: synthesization AACSB: Application of knowledge

100) Pairwise comparisons are made among: A) all alternatives for a particular criterion. B) all alternatives for all criteria. C) some alternatives for a particular criterion. D) some alternatives for all criteria. Answer: A Diff: 2 Page Ref: 432 Section Heading: The Analytical Hierarchy Process Keywords: pairwise comparisons AACSB: Application of knowledge

101) In a pairwise comparison matrix the diagonal values will ________ equal ________. A) sometimes, 1 B) always, 0 C) sometimes, 0 D) always, 1 Answer: D Diff: 2 Page Ref: 432 Section Heading: The Analytical Hierarchy Process Keywords: pairwise comparisons AACSB: Analytical thinking

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102) The analytic hierarchy process: A) optimizes procedures with a single goal. B) requires no pairwise comparison. C) uses both qualitative and subjective assessment. D) does not require the input of a decision maker. Answer: C Diff: 2 Page Ref: 430 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process AACSB: Application of knowledge

103) In determining the pairwise comparison matrix, if the decision maker rates the option A compared to option B as "4", then option B compared to option A: A) would also have to be answered by the decision maker. B) is also 4. C) is 1/4. D) is 2. Answer: C Diff: 2 Page Ref: 432 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process AACSB: Analytical thinking

104) The analytical hierarchy process is a method for ________ decision alternatives. A) creating B) ranking C) changing D) deleting Answer: B Diff: 1 Page Ref: 430 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process AACSB: Application of knowledge

105) Values with an acceptable consistency ratio are values: A) less than or equal to 0.1. B) greater than 0.5 but less than 0.6. C) less than 1 but greater than 0.5. D) greater than 0.2 but less than 0.5. Answer: A Diff: 2 Page Ref: 439 Section Heading: The Analytical Hierarchy Process Keywords: graphical solution to a goal programming problem AACSB: Application of knowledge

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106) Assume that a decision maker has to make a choice between three types of cars. Chevy, Honda, and Ford. Based on three criteria: comfort, MPG, and style. The row averages for criteria is summarized in the following column vector:

The first row of the following matrix represents Chevy, the second row represents Honda, and the third row represents Ford. The preference matrix for the three types of cars is given as follows:

Compute the overall score for each decision alternative (car). Which choice does the decision maker prefer? A) Chevy B) Honda C) Ford D) Honda and Chevy are equally preferred. Answer: B Diff: 3 Page Ref: 435 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process solution method, calc of overall scores AACSB: Analytical thinking

107) Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Cleveland, and St. Louis. The following pairwise comparison matrix summarizes the preferences of the plant manager.

Detroit Cleveland St. Louis

Detroit 1 3 4

Cleveland 1/3 1 2

St. Louis 1/4 1/2 1

Which choice does the decision maker prefer? A) Detroit B) Cleveland C) St. Louis D) Cleveland and St. Louis are equally preferred. Answer: C Diff: 3 Page Ref: 435 Section Heading: The Analytical Hierarchy Process Keywords: pairwise comparison, normalized matrix AACSB: Analytical thinking

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108) Three fast food restaurants on a college campus have been subjected to pairwise comparisons on the quality of their food. The matrix is: Pizza Mama's Papa's Freddie's

Mama's 1

Papa's 3 1

Freddie's 8 4 1

Which choice does the decision maker prefer? A) Mama's B) Papa's C) Freddie's D) This cannot be determined from the information provided. Answer: A Diff: 3 Page Ref: 435 Section Heading: The Analytical Hierarchy Process Keywords: pairwise comparison, normalized matrix AACSB: Analytical thinking

109) In the ________ process, the decision maker determines how well each alternative scores on a criterion using pairwise comparisons. A) linear programming B) simplex tableau C) goal programming D) analytical hierarchy Answer: D Diff: 2 Page Ref: 432 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process AACSB: Application of knowledge

110) A required step in the analytic hierarchy process is to determine the: A) number of hierarchies to use. B) relative importance of a set of features based on a criterion. C) goals to be satisfied. D) expected value of the criteria. Answer: B Diff: 2 Page Ref: 433 Section Heading: The Analytical Hierarchy Process Keywords: analytical hierarchy process AACSB: Application of knowledge

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111) An art critic is evaluating four different interpretations of "The Nutcracker". The pairwise comparison matrix for the criterion "originality of choreography" is given below. Choreographer A B C D

A 1 3 1/3 1/4

B 1/3 1 1/5 1/2

C 3 5 1 1/6

D 4 2 6 1

Determine the priorities of the four choreographers relative to "originality." A) A is preferred to B; B is preferred to C; and C is preferred to D. B) B is preferred to A; A is preferred to D; and D is preferred to C. C) B is preferred to A; A is preferred to C; and C is preferred to D. D) C is preferred to A; A is preferred to D; and D is preferred to B. Answer: C Diff: 2 Page Ref: 432 Section Heading: The Analytical Hierarchy Process Keywords: pairwise comparisons AACSB: Analytical thinking

112) In synthesization, dividing each value in each column of the pairwise comparison matrix by the corresponding column sum, we obtain the ________ matrix. A) pairwise B) normalized C) preference D) criteria Answer: B Diff: 2 Page Ref: 433 Section Heading: The Analytical Hierarchy Process Keywords: synthesization, normalized matrix AACSB: Application of knowledge

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113) Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Cleveland, and St. Louis. The company has weighted each of these criteria in terms of its relative importance in the decision making process, and it has analyzed each potential warehouse location and graded them according to each criteria as shown in the following table.

Decision Criteria

Weight

Proximity to suppliers Proximity to customers Land and construction costs

.45 .35 .20

Grades for Grades for Grades for Detroit Cleveland St. Louis 80 70 60 75 90 80 60 50 85

From the scores for each location, determine where the warehouse should be located. A) Detroit B) Cleveland C) St. Louis D) Cleveland and St. Louis are equally preferred. Answer: A Diff: 2 Page Ref: 433 Section Heading: Scoring Models Keywords: scoring model AACSB: Analytical thinking

114) A business is trying to decide which restaurant to hold its annual awards banquet. Use the information below to determine the best choice.

Criteria Appearance Service Atmosphere Location Quality of food

Weight 0.15 0.30 0.15 0.10 0.30

A 40 75 60 90 70

Restaurant B C 65 60 80 70 40 70 100 75 80 75

Where should the restaurant be located? A) A B) B C) C D) A and B equally preferred. Answer: B Diff: 2 Page Ref: 433 Section Heading: Scoring Models Keywords: scoring AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 10 Nonlinear Programming 1) The slope of a curve at any point is equal to the derivative of the curve's function. Answer: TRUE Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming AACSB: Analytical thinking

2) The slope of a curve at its highest point equals 1. Answer: FALSE Diff: 1 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming AACSB: Analytical thinking

3) A profit function of Z = 3x2 - 12x + 5 reaches maximum profit at x = 2 units of output. Answer: TRUE Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming, slope of a curve (function) AACSB: Analytical thinking

4) Classical optimization uses calculus to determine the optimal values of a variable. Answer: TRUE Diff: 1 Page Ref: 490 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming, slope of a curve (function) AACSB: Application of knowledge

5) A firm has a cost function of 3x2 - 25x + 374. Without having two examples of their output volume and total cost, we cannot determine their fixed cost. Answer: FALSE Diff: 1 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming, slope of a curve (function) AACSB: Analytical thinking

6) Maximum profit is achieved everywhere the first derivative of the profit function equals zero. Answer: FALSE Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming, slope of a curve (function) AACSB: Analytical thinking

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7) The first derivative of a cost function equals zero at the point V = 100. This is definitely the worst output volume for the producer to choose. Answer: FALSE Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming, slope of a curve (function) AACSB: Analytical thinking

8) Decision variables cannot be multiplied by each other in the objective function of a nonlinear program. Answer: FALSE Diff: 1 Page Ref: 490 Section Heading: Constrained Optimization Keywords: nonlinear programming AACSB: Application of knowledge

9) Both linear and nonlinear programming models are examples of constrained optimization models. Answer: TRUE Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: constrained optimization AACSB: Application of knowledge

10) An optimal solution to a nonlinear programming problem will always occur at the boundary of the feasible solution space formed by the constraint. Answer: FALSE Diff: 2 Page Ref: 492 Section Heading: Constrained Optimization Keywords: nonlinear programming problem AACSB: Analytical thinking

11) The Lagrange multiplier is analogous to the dual variables in a linear programming problem. Answer: TRUE Diff: 3 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrange multiplier AACSB: Analytical thinking

12) The Lagrange multiplier at the optimum gives only the instantaneous rate of change in the objective value. Answer: TRUE Diff: 3 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrange multiplier AACSB: Analytical thinking

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13) Both linear and nonlinear programming models have the general form of an objective function subject to more than 1 constraint. Answer: FALSE Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: nonlinear programming, model formulation AACSB: Application of knowledge

14) Classical optimization is the use of calculus to determine the optimal value of a variable. Answer: TRUE Diff: 2 Page Ref: 490 Section Heading: Nonlinear Profit Analysis Keywords: classical optimization AACSB: Application of knowledge

15) If a nonlinear program has been correctly formulated, procedures guarantee a solution. Answer: FALSE Diff: 3 Page Ref: 492 Section Heading: Constrained Optimization Keywords: nonlinear programming problem AACSB: Application of knowledge

16) In an unconstrained nonlinear programming problem, we have a single nonlinear objective function and no constraints. Answer: TRUE Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: unconstrained nonlinear programming problem AACSB: Application of knowledge

17) Constraints for nonlinear programs are usually nonlinear. Answer: FALSE Diff: 2 Page Ref: 491 Section Heading: Constrained Optimization Keywords: constrained nonlinear programming AACSB: Application of knowledge

18) In portfolio selection problems, risk is measured by the variance of the return on the portfolio. Answer: TRUE Diff: 2 Page Ref: 500 Section Heading: Nonlinear Model Examples Keywords: portfolio selection problems AACSB: Analytical thinking

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19) In solving the facility location problem, the objective is to locate a centralized facility that serves customers or other facilities such that the distance traveled between the facility and customers or other facilities is minimized. Answer: TRUE Diff: 2 Page Ref: 499 Section Heading: Nonlinear Model Examples Keywords: facility location AACSB: Application of knowledge

20) If a nonlinear programming model consists of a single nonlinear objective function and a single linear constraint, it is called a(n) ________ optimization problem. Answer: constrained or nonlinear Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: constrained, nonlinear programming problem AACSB: Application of knowledge

21) If a nonlinear programming model consists of a single nonlinear objective function and no constraints, it is called a(n) ________ optimization problem. Answer: unconstrained Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: unconstrained nonlinear programming problem AACSB: Application of knowledge

22) The ________ reflects the approximate change in the objective function resulting from a unit change in the quantity (right-hand-side) value of the constraint. Answer: Lagrange multiplier Diff: 2 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrange multiplier AACSB: Analytical thinking

23) The dual value of a resource in a nonlinear programming model is given by the ________. Answer: Lagrange multiplier Diff: 2 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrangian function AACSB: Application of knowledge

24) Assume a nonlinear programming problem with a single constraint has been solved. The value of the Lagrange multiplier is $0.75 and the value of the optimal profit (Z) is $25. If the right-hand side of the constraint is increased from 38 to 42, the new value of Z will be ________. Answer: $28 Diff: 2 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrange multiplier AACSB: Analytical thinking

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25) If a nonlinear programming problem results in profit (Z) of $50, and the Lagrange multiplier for a constraint is -2, the new profit will be ________ if the right-hand side of the constraint is increased by 1 unit. Answer: $48 Diff: 1 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrange multiplier AACSB: Analytical thinking

26) If a firm's profit is Z = 100p -8p2 +16, then the maximum profit occurs where p = ________. Answer: 6.25 Diff: 2 Page Ref: 487-488 Section Heading: Nonlinear Profit Analysis Keywords: solution to unconstrained nonlinear programming problem AACSB: Analytical thinking

27) If a firm's profit is Z = 20p -2p2 + 40, then the optimal value of I yields a maximum profit of ________. Answer: 90 (p=5) Diff: 2 Page Ref: 487-488 Section Heading: Nonlinear Profit Analysis Keywords: solution to unconstrained nonlinear programming problem AACSB: Analytical thinking

28) Assume price and demand are related by the following function: v = 200 - p. If fixed cost = $10,000 and variable cost = $8, then the expression for profit is ________. Answer: Z = 208p - p2 - 11,600 Diff: 2 Page Ref: 487-488 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming AACSB: Analytical thinking

29) Assume price and demand are related by the following function: v = 100 - 2.5p. If fixed cost = $5000 and variable cost = $10, then the expression for profit is ________. Answer: Z = 125p - 2.5p2 - 6000 Diff: 2 Page Ref: 487-488 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming AACSB: Analytical thinking

30) If price and demand are related by the function v = 15 + 15p and the fixed cost is $150 while the variable cost is $5, then the expression for profit is ________. Answer: Z = 15 p2 - 60p - 225 Diff: 2 Page Ref: 487-488 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming AACSB: Analytical thinking

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31) If price and demand are related by the function v = 15 + 15p and the fixed cost is $150 while the variable cost is $5, then the profit at a price of 20 Rupees is ________. Answer: 4575 Rupees Diff: 2 Page Ref: 487-488 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming AACSB: Analytical thinking

32) ________, a measure of correlation between returns on investment i and returns on investment j is used to reflect risk. Answer: Covariance Diff: 2 Page Ref: 500 Section Heading: Nonlinear Model Examples Keywords: portfolio selection model, covariance, risk management AACSB: Application of knowledge

33) The ________ of the value of investment is a measure of risk. Answer: variance Diff: 2 Page Ref: 500 Section Heading: Nonlinear Model Examples Keywords: portfolio selection model, variance, risk management AACSB: Application of knowledge

34) The ________ the variability in an investment portfolio, the ________ the risk of the investment portfolio. Answer: higher, higher OR lower, lower Diff: 2 Page Ref: 500 Section Heading: Nonlinear Model Examples Keywords: portfolio selection model, variance, risk management AACSB: Application of knowledge

35) The ________ measure of distance between two points on a set of X and Y coordinates is the hypotenuse of a right triangle. Answer: straight line (direct, Euclidian) Diff: 2 Page Ref: 499 Section Heading: Nonlinear Model Examples Keywords: facility location, distance measurement AACSB: Application of knowledge

36) The objective of a facility location problem is to minimize ________. Answer: the total distance traveled Diff: 1 Page Ref: 499 Section Heading: Nonlinear Model Examples Keywords: facility location, distance measurement AACSB: Application of knowledge

6 .

37) The distance formula of d =

will find the ________ distance between two

locations. Answer: straight line Diff: 1 Page Ref: 499 Section Heading: Nonlinear Model Examples Keywords: facility location, distance measurement AACSB: Analytical thinking

38) The first derivative of the fixed cost line is ________. Answer: zero Diff: 1 Page Ref: 488 Section Heading: Nonlinear Profit Analysis Keywords: derivative of the curve's function, slope of a curve AACSB: Analytical thinking

The XYZ manufacturing company produces ball bearings. The annual fixed cost is $20,000 and the variable cost per ball bearing is $3. The price is related to demand according to the following equation: 1000 - 8p. 39) What is the nonlinear profit function for the XYZ company? Simplify the terms as much as possible. Answer: Z = 1024p - 8p2 - 23,000 Diff: 2 Page Ref: 488 Section Heading: Nonlinear Profit Analysis Keywords: obj function of a nonlinear prog prob, calc of objective function AACSB: Analytical thinking

40) What is the derivative of the profit function for the XYZ company? Simplify the terms as much as possible. Answer:

= 1024 - 16p

Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: obj function of nonlinear prog prob, derivative of the function AACSB: Analytical thinking

41) What price for the ball bearings will maximize the profit? Answer: 64 Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: solution to unconstrained nonlinear prog prob, optimal price AACSB: Analytical thinking

42) What is the optimal production quantity? Answer: 488 units Diff: 3 Page Ref: 480 Section Heading: Nonlinear Profit Analysis Keywords: solution to unconstrained nonlinear prog prob, optimal price AACSB: Analytical thinking

7 .

43) What is the optimal profit? Answer: $9768 Diff: 3 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: solution to unconstrained nonlinear prog prob, optimal price AACSB: Analytical thinking

The Salt Creek Soap Company has determined the following nonlinear model to determine the optimal pounds of industrial soap (X1) and shampoo (X2) it should produce each day. Maximize Z = X12 + 2X22 - 8X1 - 12X2 + 34 Subject to: X1 + 2X2 = 4 lbs 44) Determine the quantity of soap and shampoo that should be produced to maximize profit. Answer: X1 = 0, X2 = 2 Diff: 3 Page Ref: 492-494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: solution-constrained nonlinear prog prob, optimal variable values AACSB: Analytical thinking

45) Determine the profit for the optimal production quantities of soap and shampoo. Answer: Z = 18 Diff: 3 Page Ref: 492-494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: solution to constrained nonlinear prog problem, optimal profit AACSB: Analytical thinking

46) Lush Lawns, Inc. provides a lawn fertilizer and weed control service. They are adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A budget of $2000 is to be used on this promotional campaign over the next quarter. Based on past experience in promoting its other services, Lush Lawns has been able to obtain an estimate of the relationship between sales and the amount spent on promotion in these two media: s = 2x12 - 10x22 - 2x1x2 + 18x1 + 34x2 s.t. x1 + x2 = 2 Solve. Answer: x1 = 1.66; x2 = 0.33, Lagrange multiplier = 24 Diff: 3 Page Ref: 492-494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: solution to constrained nonlinear program AACSB: Analytical thinking

8 .

Zevon Enterprises Zevon Enterprises provides services for clients worldwide and to protect all parties to this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of these services has its own special mix of needs for the resources the company has at its disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2 product requires two lawyers, five guns, and $4,000; and the X 3 product requires four lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and $15,000,000. For ease of conversation, Zevon employees usually speak about dollars as "per thousand" so one of them asking for $7 means that they really need $7,000. Zevon's demand is variable depending on what they charge for it. For example, the X 1 product's demand is 200 - 2.25p1. The demand for X2 is 300 - 3p2, and the demand for X3 is 400 - 3.5p3. The per unit profit forX1 through X3 can be calculated by subtracting the per unit cost from the sales price, so for X 1, the profit is p1 - 2.25, for X2 the profit is p2 - 3, and for X3 the profit is p3 - 3.5. 47) Formulate an appropriate objective function for this scenario. Answer: Max Z = (p1 - 2.25)X1 + (p2 - 3)X2 + (p3 - 3.5)X3 Diff: 3 Page Ref: 496 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

48) Formulate the lawyer constraint for this scenario. Answer: The lawyer constraint is as follows: 3X1 + 2X2 + 4X3 ≤ 5,000 where: X1 = 200 - 2.25p1 X2 = 300 - 3.00p2 X3 = 400 - 3.50p3 Diff: 2 Page Ref: 496 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

49) Formulate the financial constraint for this scenario. Answer: 6X1 + 4X2 + 7X3 ≤ 15,000 where: X1 = 200 - 2.25p1 X2 = 300 - 3.00p2 X3 = 400 - 3.50p3 p1 = price of X1 p2 = price of X2 p3 = price of X3 Diff: 2 Page Ref: 496 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

9 .

50) Formulate the objective function and constraints for this scenario. Answer: Max Z = (p1-2.25)X1 + (p2-3)X2 + (p3-3.5)X3 subject to: 3X1 + 2X2 + 4X3 ≤ 5,000 7X1 + 5X2 + 6X3 ≤ 10,000 6X1 + 4X2 + 7X3 ≤ 15,000 where: X1 = 200 - 2.25p1 X2 = 300 - 3.00p2 X3 = 400 - 3.50p3 p1 = price of X1 p2 = price of X2 p3 = price of X3 Diff: 3 Page Ref: 496 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

51) The model was entered into an Excel spreadsheet and the table below shows part of the sensitivity report. Provide an interpretation. Constraints Cell

Name

Final Value

$F$8 $F$9 $F$10

Lawyers Guns Money

1358.906273 2573.031361 2523.937562

Lagrange Multiplier 0 0 0

Answer: The model provides a solution that calls for only 1358.9 lawyers, 2573.03 guns and 2523.9 thousands of dollars, far below the amount on hand for this endeavor. The Lagrange Multipliers are all zero, which reflects the lack of urgency in acquiring more lawyers, guns, and money. Since Zevon is not using all that they already have, there is no benefit to acquiring any more of these resources. Diff: 2 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

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52) The model was entered into an Excel spreadsheet and the table below shows part of the sensitivity report. Calculate the expected per unit profit for the three services. Variable Cells Cell

Name

Final Value

$C$3 $D$3 $E$3

P1_ P2_ P3_

45.5694 51.5 58.8929

Reduced Gradient 0 0 0

Answer: The model provides a solution that calls for only a sale price for P 1 of $45.57 - coupled with its price of $2.25 means they make $43.32 per unit of X1. For item X2, the optimal price is $51.50, less the cost of $3, means Zevon makes $48.50 per unit. Finally, X3 will sell for $58.89, less the price of $3.50 means they realize a profit of $55.39 per unit. Diff: 2 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

53) The model was entered into an Excel spreadsheet and the table below shows part of the answer report. Provide an interpretation. Constraints Cell

Name

Cell Value

$F$8 Lawyers $F$9 Guns $F$10 Money

1358.906273 2573.031361 2523.937562

Formula

Status

$F$8<=$I$8 Not Binding $F$9<=$I$9 Not Binding $F$10<=$I$10 Not Binding

Slack 3641.093727 7426.968639 12476.06244

Answer: The model provides a solution that calls for only 1359 lawyers out of the 5000 available, meaning Zevon has 3641 lawyers that are not assigned to this model. Similarly, only 2573 guns and $2,523,973.56 are needed out of the 10,000 guns and $15,000,000 available to them. Diff: 1 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

11 .

54) The model was entered into an Excel spreadsheet and the table below shows the answer report in its entirety. Show how the profit is calculated. Objective Cell (Max) Cell

Name

Original Value

Final Value

$F$4

Profit

$5,638.13

$22,018.33

Variable Cells Cell

Name

Original Value

Final Value

Integer

$C$3 $D$3 $E$3

P1_ P2_ P3_

$10.00 $10.00 $10.00

$45.57 $51.50 $58.89

Contin Contin Contin

Formula

Status

Constraints Cell

Name

$F$8 Lawyers $F$9 Guns $F$10 Money

Cell Value 1358.91 2573.03 2523.94

$F$8<=$I$8 Not Binding $F$9<=$I$9 Not Binding $F$10<=$I$10 Not Binding

Slack 3641.09 7426.97 12476.06

Answer: The profit is a function of quantity sold and price, with the quantity sold a function of price. The X1 product has a demand of 200 - 2.25 × 45.57 = 97 The X2 product has a demand of 300 - 3 × 51.50 = 146 The X3 product has a demand of 400 - 3.5 × 58.89 = 194 The profit per X1 is $45.57 - 2.25 = $43.32 The profit per X2 is $51.50 - 3 = $48.50 The profit per X3 is $58.89 - 3.5 = $55.39 So 97 × $43.32 + 146 × $48.50 + 194 × 55.39 = $22,018.33 Diff: 1 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

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55) The analytics gurus at Zevon realize that they had misformulated their demand curves. They now believe that demand for X1 is given by 1000 - 2.25p1, demand for X2 is given by 2000 - 3p2, and demand for X3 is given by 3000 - 3.5p3. This model is entered in Excel and the sensitivity report contains the following: Constraints Name

Final Value

Lagrange Multiplier

$F$8 Lawyers $F$9 Guns $F$10 Money

5000.00 9275.74 9213.49

101.052 0 0

Cell

Provide an interpretation of all elements. Answer: The only resource that Zevon could use more of is lawyers; the final value is 5000, which exhausts their entire supply. If additional lawyers could be retained for less than $101.05, then Zevon should pursue this possibility. There is no information available as to the range for the validity of this $101.05. The guns resource has only 725 units remaining and the money resource has $5,800 left. When one of those two resources is exhausted, the lawyer Lagrange multiplier will likely not be valid. Diff: 2 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

13 .

Mad Over Donuts An entrepreneurial resident of the Oklahoma City metropolitan area is interested in securing a new franchise for Mad Over Donuts. Ideally this franchise would be centrally located so delivery could be economically handled and all citizens could enjoy fresh, delicious donuts delivered to the doorstep. The main cities and anticipated demand (in thousands per day) are shown in the table. City Jones Luther Harrah Edmond Norman Moore

x-coord 6 13 12 0 2 3

y-coord 28 35 22 32 0 8

Demand 45 56 30 25 33 22

56) What is the appropriate objective function for this scenario? Answer: The objective function is: Min Z = where d= and t = the number of trips (demand) i Diff: 2 Page Ref: 499 Section Heading: Nonlinear Model Examples Keywords: nonlinear programming AACSB: Analytical thinking

57) What are the appropriate constraints for this scenario? Answer: There are no constraints for this model. It is a nonlinear unconstrained optimization problem. Diff: 2 Page Ref: 500 Section Heading: Nonlinear Model Examples Keywords: nonlinear programming AACSB: Analytical thinking

58) Zoey's Catnip Toys faces the following relationship between price and demand: v = 2000 - 200p. The fixed cost is $500 and variable cost is $1. Write an expression for the total profit. Answer: Z = 2200p - 200p2 - 2500 Diff: 2 Page Ref: 487 Section Heading: Nonlinear Profit Analysis Keywords: obj function of nonlinear prog problem, calculation of obj function AACSB: Analytical thinking

59) Zoey's Catnip Toys faces the following relationship between price and demand: v = 2000 - 200p. The fixed cost is $500 and variable cost is $1. What price should Zoey charge to maximize profit? Answer: $5.50 Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: solution to constrained nonlinear program AACSB: Analytical thinking

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Sara's Sensible Critters makes two kinds of catnip toys: balls (x1) and mice (x2). The relationship between demand and price for balls and mice is: x1 = 1800 - 150p1 x2 = 1500 - 300p2 The cost for a catnip ball is $2 and for the mouse, $3. Sara has only 200 ounces of catnip on hand. A ball uses a tenth of an ounce and a toy mouse uses onequarter of an ounce. 60) Write the formulation for this problem Answer: Max Z = (p1 - 2)x1 + (p2 - 3)x2 s.t. 0.10x1 + 0.25x2 ≤ 200 Alternatively, Z = 2100p1 - 150p12 - 2400p2 - 300p22 - 8100 Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: solution to constrained nonlinear program AACSB: Analytical thinking

61) Determine the prices that Sara should charge to maximize profit. Answer: p1 = 7 p2 = 4 Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: solution to constrained nonlinear program AACSB: Analytical thinking

62) Sara has found an unlimited source of catnip so that is no longer a constraint. However, customer demand dictates that she produce 2.5 times more catnip balls than mice. Write the new constraint. Answer: x1 = 2.5x2 OR x1 -2.5x2 = 0 Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: solution to constrained nonlinear program AACSB: Analytical thinking

63) Sara has found an unlimited source of catnip so that is no longer a constraint. However, customer demand dictates that she produce 2.5 times more catnip balls than mice. How will this impact the prices that she should charge to maximize profit? Answer: There is no impact. Prices remain the same. Note: The optimal quantities are 750 balls and 300 mice for a profit of $4050. Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: solution to constrained nonlinear program AACSB: Analytical thinking

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64) A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x2 - 10C2 + 40Cx + 120x - 200C + 600. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales? Answer: 5 square feet Diff: 2 Page Ref: 488 Section Heading: Nonlinear Profit Analysis Keywords: solution to unconstrained nonlinear program AACSB: Analytical thinking

65) Consider the curve 7x2 - 14x + 28. What is the highest point on this curve? Answer: x = 1 Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: unconstrained nonlinear programming problem AACSB: Analytical thinking

66) Consider the curve 7x2 - 14x + 28. What is the slope at x = 5? Answer: 56 Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: derivative of the curve's function, slope of a curve AACSB: Analytical thinking

67) Consider the curve 7x2 - 14x + 28. What is the second derivative at x = 10? Answer: 7 Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: derivative of a function AACSB: Analytical thinking

68) The slope of a curve at its highest point equals: A) 0. B) 1. C) 2. D) 3. Answer: A Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: nonlinear programming, slope of a curve (function) AACSB: Application of knowledge

16 .

69) A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x2 - 10C2 + 40Cx + 120x - 200. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales? A) 3 B) 4 C) 5 D) 1 or 9 Answer: C Diff: 2 Page Ref: 487-490 Section Heading: Nonlinear Profit Analysis Keywords: solution to unconstrained nonlinear program AACSB: Analytical thinking

70) If a firm's profit is Z = 12x - 6x2 + 30, and their minimum production level of x is equal to 0.5, then the level of x that maximizes profit is: A) .5. B) 1. C) 1.5. D) 2. Answer: B Diff: 2 Page Ref: 487-490 Section Heading: Nonlinear Profit Analysis Keywords: solution to constrained nonlinear programming problem AACSB: Analytical thinking

71) A custom molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 - 5x1, and the per unit contribution for the cocktail glasses (x2) is 80 - 4x2. An expression for the total contribution is: A) 20 - 4x2 - 5x1. B) 60x1 - 5x12 + 80x2 - 4x22. C) 80x1 - 5x12 + 60x2 - 4x22. D) 20 - (4x2)(5x1). Answer: B Diff: 2 Page Ref: 487 Section Heading: Nonlinear Profit Analysis Keywords: obj function of nonlinear prog problem, calculation of obj function AACSB: Analytical thinking

17 .

72) Classical optimization is the use of ________ to determine the optimal value of a variable. A) calculus B) linear programming C) nonlinear programming D) goal programming Answer: A Diff: 1 Page Ref: 490 Section Heading: Nonlinear Profit Analysis Keywords: classical optimization AACSB: Application of knowledge

73) The derivative of a function ________ the slope of the curve defined by that function. A) is larger than B) equals C) is smaller than D) is similar to Answer: B Diff: 2 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: slope of a curve AACSB: Application of knowledge

74) Both linear and nonlinear programming models are examples of: A) goal programming models. B) simplex tableaus. C) constrained likelihood models. D) constrained optimization models. Answer: D Diff: 2 Page Ref: 490 Section Heading: Constrained Optimization Keywords: constrained optimization models AACSB: Application of knowledge

75) The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the ________ of the constraint equation. A) coefficient B) objective function C) right-hand side D) shadow price Answer: C Diff: 2 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrange multiplier AACSB: Application of knowledge

18 .

76) The Lagrange multiplier is ________ to the dual variables in a linear programming problem. A) analogous B) contradictory C) inversely related D) opposite Answer: A Diff: 3 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrange multiplier AACSB: Application of knowledge

77) The Lagrange multiplier is: A) the shadow price for the constraint coefficients. B) valid over a range of changes in the RHS. C) the rate of change in the objective value as the RHS of the constraint increases. D) the minimum threshold for decision variables to enter the solution. Answer: C Diff: 2 Page Ref: 494 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: Lagrange multiplier AACSB: Application of knowledge

78) The XYZ manufacturing company produces ball bearings. The annual fixed cost is $20,000 and the variable cost per ball bearing is $3. The price is related to demand according to the following equation: v = 1000 - 8p. What is the optimal price of the ball bearings that will maximize the profit? A) $47.99 B) $53.99 C) $58.99 D) $63.99 Answer: D Diff: 3 Page Ref: 487-490 Section Heading: Nonlinear Profit Analysis Keywords: solution-unconstrained nonlinear prog prob, optimal var values AACSB: Analytical thinking

79) The XYZ manufacturing company produces ball bearings. The annual fixed cost is $20,000 and the variable cost per ball bearing is $3. The price is related to demand according to the following equation: v = 1000 - 8p. What is optimal profit? A) $6668 B) $7668 C) $8668 D) $9768 Answer: D Diff: 3 Page Ref: 489 Section Heading: Nonlinear Profit Analysis Keywords: solution to unconstrained nonlinear prog prob, optimal profit AACSB: Analytical thinking

19 .

Zevon Enterprises Zevon Enterprises provides services for clients worldwide and to protect all parties to this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of these services has its own special mix of needs for the resources the company has at its disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2 product requires two lawyers, five guns, and $4,000; and the X 3 product requires four lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and $15,000,000. For ease of conversation, Zevon employees usually speak about dollars as "per thousand" so one of them asking for $7 means that they really need $7,000. Zevon's demand is variable depending on what they charge for it. For example, the X 1 product's demand is 200 - 2.25p1. The demand for X2 is 300 - 3p2, and the demand for X3 is 400 - 3.5p3. The per unit profit forX1 through X3 can be calculated by subtracting the per unit cost from the sales price, so for X 1, the profit is p1 - 2.25, for X2 the profit is p2 - 3, and for X3 the profit is p3 - 3.5. 80) What is an appropriate objective function for this scenario? A) Max Z = (p1 - 2.25)X1 + (p2 - 3)X2 + (p3 - 3.5)X3 B) Max Z = (p1 - 2.25)(200 - 2.25p1) + (p2 - 3)(300 - 3.00p2) + (p3 - 3.5)(400 - 3.50p3) C) Max Z = 200X1 + 300X2 + 400X3 D) Max Z = 2.25(p1 - X1) + 3(p2 - X2) +3.5 (p3 - X3) Answer: A Diff: 3 Page Ref: 496-498 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

81) Which of these is the lawyer constraint for this scenario? A) 7X1 + 5X2 + 6X3 ≤ 10,000 B) 3X1 + 2X2 + 4X3 ≤ 5,000 C) 6X1 + 4X2 + 7X3 ≤ 15,000 D) X1 = 200 - 2.25p1 Answer: B Diff: 1 Page Ref: 496-498 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

82) Which of these is the money constraint for this scenario? A) 7X1 + 5X2 + 6X3 ≤ 10,000 B) 3X1 + 2X2 + 4X3 ≤ 5,000 C) 6X1 + 4X2 + 7X3 ≤ 15,000 D) X1 = 200 - 2.25p1 Answer: C Diff: 1 Page Ref: 496-498 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

20 .

83) The model is entered in Excel and executes to reveal that p1 equals $45.57. Which of these conclusions is correct? A) The per unit profit for X1 is $45.57. B) The contribution to net profit from service X1 is $4,441.59. C) There is excess demand for service X1. D) The demand for X1 is 97. Answer: D Diff: 2 Page Ref: 496-498 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

84) The model is entered in Excel and executes to reveal that p2 equals $51.50. Which of these conclusions is correct? A) The contribution to net profit from service X2 is $7,056.75. B) The per unit profit for service X2 is $51.50. C) There is excess demand for service X1. D) The demand for X2 is 194. Answer: A Diff: 2 Page Ref: 496-498 Section Heading: A Nonlinear Programming Model with Multiple Constraints Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

85) The model is entered in Excel and the sensitivity report reveals that all of the constraints' Lagrange multipliers are zero. The impact for Zevon is: A) The profit for this scenario cannot be maximized. B) Not all of the lawyers they have available will be used. C) The demand for service X1 exceeds Zevon's ability to supply it. D) The profit generated by service X1 is not a function of demand for X1. Answer: B Diff: 1 Page Ref: 493-495 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

21 .

86) The analytics gurus at Zevon realize that they had misformulated their demand curves. They now believe that demand for X1 is given by 1000 - 2.25p1, demand for X2 is given by 2000 - 3p2, and demand for X3 is given by 3000 - 3.5p3. This model is entered in Excel and the sensitivity report contains the following: Constraints Name

Final Value

Lagrange Multiplier

$F$8 Lawyers $F$9 Guns $F$10 Money

5000.00 9275.74 9213.49

101.052 0 0

Cell

What is the best conclusion from the list below? A) The profit for this scenario cannot be maximized. B) Not all of the lawyers they have available will be used. C) If Zevon can retain the services of another lawyer for less than $101, they should do so. D) Lawyer jokes aside, Zevon cannot benefit from hiring additional lawyers at any cost. Answer: C Diff: 2 Page Ref: 493-495 Section Heading: Solution of Nonlinear Programming Problems with Excel Keywords: nonlinear programming, model formulation AACSB: Analytical thinking

The Salt Creek Soap Company has determined the following nonlinear model to determine the optimal pounds of industrial soap (X1) and shampoo (X2) it should produce each day. Maximize Z = X12 + 2X22 - 8X1 - 12X2 + 34 Subject to: X1 + 2X2 = 4 lbs 87) What quantities of soap and shampoo maximize profit? A) X1 = 0, X2 = 2 B) X1 = 1, X2 = 2 C) X1 = 2, X2 = 2 D) X1 = 2, X2 = 1 Answer: A Diff: 3 Page Ref: 490 Section Heading: Constrained Optimization Keywords: solution-constrained nonlinear prog prob, optimal variable values AACSB: Analytical thinking

22 .

88) What is profit when the optimal values of soap and shampoo are produced? A) Z = 12 B) Z = 14 C) Z = 16 D) Z = 18 Answer: B Diff: 3 Page Ref: 490 Section Heading: Constrained Optimization Keywords: solution to constrained nonlinear prog problem, optimal profit AACSB: Analytical thinking

Sara's Sensible Critters makes two kinds of catnip toys: balls (x1) and mice (x2). The relationship between demand and price for balls and mice is: x1 = 1800 - 150p1 x2 = 1500 - 300p2 The cost for a catnip ball is $2 and for the mouse, $3. Sara has only 200 ounces of catnip on hand. A ball uses a tenth of an ounce and a toy mouse uses onequarter of an ounce. 89) Write the appropriate expression for profit. A) Max Z = (p1 - 3)x1 + (p2 - 2)x2 B) Max Z = (p1 + 2)x1 + (p2 + 3)x2 C) Max Z = (p1 - 2)x1 + (p2 - 3)x2 D) Min Z = (p1 - 2)x1 + (p2 - 3)x2 Answer: C Diff: 3 Page Ref: 487-490 Section Heading: Nonlinear Profit Analysis Keywords: formulation, nonlinear programming AACSB: Analytical thinking

90) Write the appropriate expression for the demand constraint. A) 2.5x1 = x2 B) x1 - 2.5x2 ≥ 0 C) x1 + 2.5x2 ≤ 0 D) x1 = 2.5x2 Answer: D Diff: 3 Page Ref: 490 Section Heading: Nonlinear Profit Analysis Keywords: formulation, nonlinear programming AACSB: Analytical thinking

23 .

Introduction to Management Science, 12e (Taylor) Chapter 11 Probability and Statistics 1) Deterministic techniques assume that no uncertainty exists in model parameters. Answer: TRUE Diff: 1 Page Ref: 512 Section Heading: Types of Probability Keywords: deterministic techniques AACSB: Application of knowledge

2) Probabilistic techniques assume that no uncertainty exists in model parameters. Answer: FALSE Diff: 1 Page Ref: 512 Section Heading: Types of Probability Keywords: probabilistic techniques AACSB: Application of knowledge

3) Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori. Answer: TRUE Diff: 2 Page Ref: 512 Section Heading: Types of Probability Keywords: objective probabilities, classical probabilities AACSB: Application of knowledge

4) Objective probabilities that are stated after the outcomes of an event have been observed are relative frequencies. Answer: TRUE Diff: 2 Page Ref: 512 Section Heading: Types of Probability Keywords: relative frequencies AACSB: Application of knowledge

5) Relative frequency is the more widely used definition of objective probability. Answer: TRUE Diff: 1 Page Ref: 513 Section Heading: Types of Probability Keywords: relative frequencies AACSB: Application of knowledge

6) Subjective probability is an estimate based on personal belief, experience, or knowledge of a situation. Answer: TRUE Diff: 2 Page Ref: 513 Section Heading: Types of Probability Keywords: subjective probability AACSB: Application of knowledge

1 .

7) An experiment is an activity that results in one of several possible outcomes. Answer: TRUE Diff: 1 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: experiment AACSB: Application of knowledge

8) The events in an experiment are mutually exclusive if only one can occur at a time. Answer: TRUE Diff: 1 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: mutually exclusive events AACSB: Application of knowledge

9) In a given experiment, the probabilities of all mutually exclusive events sum to one. Answer: TRUE Diff: 1 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: mutually exclusive events, rules of probability AACSB: Application of knowledge

10) A set of events is collectively exhaustive when it includes all the events that can occur in an experiment. Answer: TRUE Diff: 2 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: collectively exhaustive events AACSB: Application of knowledge

11) A marginal probability is the probability of a single event occurring. Answer: TRUE Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: marginal probability AACSB: Application of knowledge

12) A Venn diagram visually displays mutually exclusive and non-mutually exclusive events. Answer: TRUE Diff: 2 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: Venn diagram AACSB: Application of knowledge

13) A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously. Answer: FALSE Diff: 2 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: joint probability AACSB: Application of knowledge

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14) A conditional probability is the probability that an event occurs given that another event has already occurred. Answer: TRUE Diff: 1 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: conditional probability AACSB: Application of knowledge

15) Conditional probabilities are shown in Venn diagrams. Answer: FALSE Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: conditional probability AACSB: Application of knowledge

16) Probability trees are used only to compute conditional probabilities. Answer: FALSE Diff: 2 Page Ref: 518 Section Heading: Statistical Independence and Dependence Keywords: probability tree, conditional probability AACSB: Application of knowledge

17) A succession of events that does not affect other events is independent. Answer: TRUE Diff: 1 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: independence AACSB: Application of knowledge

18) A binomial probability distribution indicates the probability of r successes in n trials. Answer: TRUE Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial probability distribution AACSB: Analytical thinking

19) A continuous random variable may assume only integer values within a given interval. Answer: FALSE Diff: 1 Page Ref: 526 Section Heading: Expected Value Keywords: continuous random variables AACSB: Analytical thinking

20) Seventy-two percent of all observations fall within one standard deviation of the mean if the data is normally distributed. Answer: FALSE Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

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21) Another name for the mean of a probability distribution is its expected value. Answer: TRUE Diff: 1 Page Ref: 525 Section Heading: Expected Value Keywords: expected value AACSB: Analytical thinking

22) The expected value of a discrete random variable is greater than or equal to zero. Answer: FALSE Diff: 1 Page Ref: 525 Section Heading: Expected Value Keywords: expected value AACSB: Application of knowledge

23) The variance of a discrete random variable is always greater than or equal to zero. Answer: TRUE Diff: 1 Page Ref: 525 Section Heading: Expected Value Keywords: expected value AACSB: Application of knowledge

24) The expected value of a random variable is computed by multiplying the sum of each possible value of the variable by the probability of that random variable. Answer: FALSE Diff: 1 Page Ref: 525 Section Heading: Expected Value Keywords: expected value AACSB: Analytical thinking

25) The variance of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products. Answer: FALSE Diff: 1 Page Ref: 525 Section Heading: Expected Value Keywords: variance AACSB: Analytical thinking

26) For a typical normally distributed random variable, the standard deviation is equal to the variance. Answer: FALSE Diff: 1 Page Ref: 527 Section Heading: Expected Value Keywords: normal distribution AACSB: Application of knowledge

27) A normally distributed random variable has a mean of zero and a standard deviation of one. Answer: FALSE Diff: 1 Page Ref: 526 Section Heading: Expected Value Keywords: normal distribution AACSB: Application of knowledge

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28) The standard normal distribution has a mean of one and a standard deviation of zero. Answer: FALSE Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: standard normal distribution AACSB: Application of knowledge

29) The area under the normal curve represents probability. Answer: TRUE Diff: 1 Page Ref: 527 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Application of knowledge

30) There is just as great a chance of a normally distributed random variable being over one standard deviation above the mean as there is being one standard deviation below the mean. Answer: TRUE Diff: 1 Page Ref: 527 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

31) An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than two incorrect inspections is 0.736. Answer: TRUE Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

32) In Bayesian analysis, additional information is used to alter the conditional probability of the occurrence of an event. Answer: FALSE Diff: 1 Page Ref: 523 Section Heading: Statistical Independence and Dependence Keywords: conditional probability AACSB: Application of knowledge

33) Objective probabilities that can be stated prior to the occurrence of an event are ________. Answer: classical or a priori Diff: 1 Page Ref: 512 Section Heading: Types of Probability Keywords: probabilistic techniques, objective/classical probabilities AACSB: Application of knowledge

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34) ________ probability is an estimate based on a personal belief, experience, and knowledge of a situation. Answer: Subjective Diff: 1 Page Ref: 513 Section Heading: Types of Probability Keywords: subjective probability AACSB: Application of knowledge

35) The events in an experiment are ________ if only one can occur at a time. Answer: mutually exclusive Diff: 1 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: mutually exclusive events AACSB: Application of knowledge

36) The term for including all possible events that can occur in an experiment is ________. Answer: collectively exhaustive Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: collectively exhaustive AACSB: Application of knowledge

37) The cumulative probability for all six outcomes of tossing a fair die should end with the value ________. Answer: 1.00 Diff: 1 Page Ref: 517 Section Heading: Fundamentals of Probability Keywords: cumulative probability distribution AACSB: Analytical thinking

38) The fact that the first toss of a coin has no effect on the outcome of the second toss of the coin suggests that these events are ________. Answer: independent Diff: 1 Page Ref: 517 Section Heading: Fundamentals of Probability Keywords: independent events AACSB: Application of knowledge

39) The collectively exhaustive set of events for flipping a coin is ________. Answer: heads, tails (and possibly landing on its side) Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: collectively exhaustive AACSB: Application of knowledge

40) A ________ organizes numerical data to describe the events of an experiment. Answer: frequency distribution Diff: 1 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: frequency distribution AACSB: Application of knowledge

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41) A Venn diagram depicting two circles that do not overlap or touch in any way represents events that are ________. Answer: mutually exclusive Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: mutually exclusive events AACSB: Application of knowledge

42) A ________ is the probability of occurrence of a single event. Answer: marginal probability Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: marginal probability AACSB: Application of knowledge

43) ________ can enable one to improve marginal probabilities of the occurrence of an event by gathering additional information. Answer: Bayesian analysis Diff: 2 Page Ref: 523 Section Heading: Fundamentals of Probability Keywords: Bayesian analysis AACSB: Application of knowledge

44) A succession of events that do not affect each other are ________. Answer: independent Diff: 2 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: independence AACSB: Application of knowledge

45) A ________ probability is the probability that an event will occur given that another event has already occurred. Answer: conditional Diff: 2 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: conditional probability AACSB: Application of knowledge

46) In a binomial distribution process, there are ________ possible outcomes. Answer: two Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Application of knowledge

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47) One of the properties of the ________ distribution is that the probability of success remains constant over time. Answer: binomial Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Application of knowledge

48) Altered marginal probability of an event based on additional information is a ________ probability. Answer: posterior Diff: 2 Page Ref: 523 Section Heading: Statistical Independence and Dependence Keywords: Bayesian analysis, posterior probability AACSB: Application of knowledge

49) The ________ of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products. Answer: expected value Diff: 1 Page Ref: 525 Section Heading: Expected Value Keywords: random variables, expected value AACSB: Application of knowledge

50) If events A and B are independent, then P(AB) = ________. Answer: P(A) × P(B) Diff: 1 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: probabilistic techniques, objective/classical probabilities AACSB: Analytical thinking

51) If events A and B are independent, then P(A|B) = ________. Answer: P(A) Diff: 1 Page Ref: 518 Section Heading: Statistical Independence and Dependence Keywords: probabilistic techniques, objective/classical probabilities AACSB: Analytical thinking

52) If two events A and B are not mutually exclusive, then P(A or B) = ________. Answer: P(A) + P(B) - P(AB) Diff: 1 Page Ref: 517 Section Heading: Fundamentals of Probability Keywords: probabilistic techniques, objective/classical probabilities AACSB: Analytical thinking

53) ________ is a measure of dispersion of random variable values about the expected value. Answer: Variance Diff: 1 Page Ref: 525 Section Heading: Expected Value Keywords: random variables, variance AACSB: Application of knowledge

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54) A continuous random variable can take on a(n) ________ number of values within a given interval. Answer: infinite Diff: 2 Page Ref: 526 Section Heading: Expected Value Keywords: continuous random variables AACSB: Application of knowledge

55) The ________ test is a statistical test to see if an observed data fit a particular probability distribution. Answer: chi-square Diff: 2 Page Ref: 532 Section Heading: Expected Value Keywords: chi-square test AACSB: Application of knowledge

56) The ________ normal distribution has a mean of 0 and a standard deviation of 1. Answer: standard Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: standard normal distribution AACSB: Analytical thinking

57) Almost all of the data from a normal distribution fall within ________ standard deviations of the mean. Answer: ±3 Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: standard normal distribution AACSB: Application of knowledge

58) The expected value of the standard normal distribution is equal to ________. Answer: 0 Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: expected value, standard normal distribution AACSB: Application of knowledge

59) The standard deviation of the standard normal distribution is equal to ________. Answer: 1 Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: expected value, standard normal distribution AACSB: Application of knowledge

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Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. 60) What is the probability that Jim will be accepted at both universities? Answer: 0.09 Diff: 2 Page Ref: 516 Section Heading: Statistical Independence and Dependence Keywords: multiplication of probabilities AACSB: Analytical thinking

61) What is the probability that Jim will not be accepted at either university? Answer: 0.44 = (.55) × (.80) Diff: 2 Page Ref: 516 Section Heading: Statistical Independence and Dependence Keywords: multiplication of probabilities AACSB: Analytical thinking

62) What is the probability that Jim will be accepted by at least one of the two universities? Answer: 0.56 = 1 - [(.55) × (.80)] Diff: 2 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: multiplication of probabilities AACSB: Analytical thinking

Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category. Male (M) Female (F) Job Administrative (AD) Salaried staff (SS) Hourly staff (HS)

110 30 60

10 50 40

63) If an employee is selected at random, what is the probability that the employee is male? Answer: .667 = 200/300 Diff: 2 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: marginal probability AACSB: Analytical thinking

64) If an employee is selected at random, what is the probability that the employee is male and salaried staff? Answer: .10 = 30/300 Diff: 2 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: joint probability AACSB: Analytical thinking

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65) If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member? Answer: .625 = 50/80 Diff: 2 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: conditional probability AACSB: Analytical thinking

66) If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration Answer: .70 = 100/300 + 120/300 - 10/300 Diff: 2 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: not mutually exclusive events, addition rule AACSB: Analytical thinking

The Dean's Office keeps tracks of student complaints received each week. The probability distribution for complaints can be represented as a table as shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

p( )

.10

.15

.18

.20

.10

.07

67) What is the probability that they receive less than 3 complaints in a week? Answer: 0.43 Diff: 2 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: probability distribution AACSB: Analytical thinking

68) What is the average number of complaints received per week? Answer: 2.83 Diff: 2 Page Ref: 525 Section Heading: Expected Value Keywords: expected value, probability distribution AACSB: Analytical thinking

69) A fair die is rolled nine times. What is the probability that an odd number (1, 3, or 5) will occur less than 3 times? Answer: 0.0899 Diff: 2 Page Ref: 519 Section Heading: The Binomial Distribution Keywords: binomial distribution AACSB: Analytical thinking

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70) A fair die is rolled 8 times. What is the probability that an even number (2, 4, or 6) will occur between 2 and 4 times? Answer: 0.6016 Diff: 2 Page Ref: 519 Section Heading: The Binomial Distribution Keywords: binomial distribution AACSB: Analytical thinking

71) It was a house with seven cats, four female and three male, and the litterbox was busier than O'Hare Airport during the week of Thanksgiving. The beleaguered husband's home office was right around the corner from the laundry room, where the litterbox was kept, and heard three separate instances of use. What is the likelihood that none of the instances were the work of the male cats? Answer: .187 Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

72) It was a house with seven cats, four female and three male, and the litterbox was busier than O'Hare Airport during the week of Thanksgiving. The beleaguered husband's home office was right around the corner from the laundry room, where the litterbox was kept, and heard four separate instances of use. What is the likelihood that half of the instances were the work of the male cats? Answer: 0.35985 Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

73) The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and because he found their gentle clucking to relax him as he worked on his laptop on his deck. Their movements around his yard gave meaning to the term random walk — you literally could not predict their location from one minute to the next. His collection of birds is neatly summarized in this table. Breed Rhode Island Red Buff Orpington Barred Rock Australorp Leghorn

Rooster 2 0 0 0 1

Hen 8 5 6 6 2

What is the probability that the next chicken that joins him up on the deck is a rooster? Answer: 3/30=0.1 Diff: 1 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

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74) The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and because he found their gentle clucking to relax him as he worked on his laptop on his deck. Their movements around his yard gave meaning to the term random walk — you literally could not predict their location from one minute to the next. His collection of birds is neatly summarized in this table. Breed Rhode Island Red Buff Orpington Barred Rock Australorp Leghorn

Rooster 2 0 0 0 1

Hen 8 5 6 6 2

A Rhode Island Red just joined him up on the deck; what is the probability it is a rooster? Answer: 2/10=0.2 Diff: 1 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of "success" is 80%. Assume that the probability of success is independent for each product. 75) Find the probability that exactly 1 of the 3 products is successful. Answer: (3)(.8)(.2)(.2) = .096 Diff: 2 Page Ref: 519 Section Heading: The Binomial Distribution Keywords: binomial distribution AACSB: Analytical thinking

76) Find the probability that none of the 3 products is successful. Answer: (1)(.2)(.2)(.2) = .008 Diff: 2 Page Ref: 519 Section Heading: The Binomial Distribution Keywords: binomial distribution AACSB: Analytical thinking

77) If X has the following probability distribution X P(X)

1 .1

2 .5

3 .2

4 .2

Compute the expected value of X. Answer: 2.5 EV = (1)(.1) + (2)(.5) + (3)(.2) + (4)(.2) = 2.5 Diff: 2 Page Ref: 525 Section Heading: Expected Value Keywords: expected value AACSB: Analytical thinking

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78) Assume X has the following probability distribution: X P(X)

1 .1

2 .5

3 .2

4 .2

Compute the standard deviation of X. Answer: .9219 Diff: 2 Page Ref: 526 Section Heading: Expected Value Keywords: standard deviation AACSB: Analytical thinking

79) If x is normally distributed with a mean of 10 and a standard deviation of 3, then P(x ≤ 6) is equal to P( Z ≤ _____)? Answer: -4/3 Diff: 3 Page Ref: 528 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

80) For a standard normal distribution, what is the probability that z is greater than 1.75? Answer: 0.0401 Diff: 3 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

Two psychology majors, in two different sections of Clinical Psychology, were comparing test scores. The following gives the students' scores, class mean, and standard deviation for each section:

Student score Mean Standard deviation

Section 1 84 75 7

Section 2 75 60 8

81) What is the z-score of the student from section 1 and what is the probability that a student in section 1 will score higher than 84? Answer: 1.286 and .0985 Diff: 3 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

82) What is the z-score of the student from section 2 and what is the probability that a student in section 2 will score higher than 75? Answer: 1.875 and .0301 Diff: 3 Page Ref: 529 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

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83) Which student scored better compared to the rest of their section? Answer: section 2 student because their z-score is higher Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: mean, standard deviation AACSB: Analytical thinking

84) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz? Answer: 0.9772 Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

85) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf of bread is larger than 23 oz? Answer: 0.0228 Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

86) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is less than 24 oz? Answer: 1 Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

87) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 20.75 and 23.25 oz? Answer: 0.9876 Diff: 2 Page Ref: 530 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

88) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 21.75 and 22.25 oz? Answer: 0.3830 Diff: 2 Page Ref: 530 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

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89) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 24 oz? Answer: 0 Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

90) The weight of a loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 22.25 oz? Answer: 0.3085 Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

91) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75? Answer: 0.0401 Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

92) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the participants die before they reach the age of 65? Answer: 0.2266 Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

93) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. By what age have 80% of the plan participants passed away? Answer: 71.36 years old Diff: 3 Page Ref: 530 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

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94) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations? Answer: 95% Diff: 1 Page Ref: 530 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

95) What is the area under the normal curve for Z ≥ 1.79? Answer: 0.0367 Diff: 3 Page Ref: 530 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

96) A study of a company's practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled 5 days. Assuming that the distribution is normal, what percent of the invoices is paid within 15 days of receipt? Answer: 15.87% Diff: 3 Page Ref: 528 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

97) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of the crabs are normally distributed, what is the probability that a randomly selected crab will weigh more than 2.2 pounds? Answer: 0.0668 Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

98) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crabs are normally distributed, what is the probability that a randomly selected crab will weigh between 1 and 2 pounds? Answer: 0.7745 Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

99) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crabs are normally distributed, the probability that a randomly selected crab will weigh less than 1.2 pounds is ________. Answer: 0.1587 Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

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100) A research scientist has observed the monkeys of the Nandi Hills outside of Bangalore for the last twenty years, carefully cataloging their preferences for a number of food items. An unsuspecting tourist leaves his can of soda unattended. Describe the type of probability the research scientist can assign to the likelihood that the soda will become the monkey's next meal. Then contrast this type of probability with the other of the two basic types. Answer: The two types of probability are objective and subjective. Objective probabilities can be stated prior to the occurrence of an event and since the scientist has observed these monkeys for twenty years, there are relative frequency probabilities associated with common items such as a can of soda. The other type of probability is subjective, which is an estimate based on personal belief. Since the scientist is experienced, this would not be an appropriate characterization of the event. We could assume the tourist is unfamiliar with the behavior of these monkeys, thus the tourist's estimate would most likely be subjective (unless the tourist was a primate research scientist on holiday). Diff: 1 Page Ref: 512 Section Heading: Types of Probability Keywords: objective probabilities, classical probabilities AACSB: Analytical thinking

101) A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of sixty six weeks and a standard deviation of ten weeks. The next career begins on Monday; what is the likelihood that it endures for less than a year and a half? Answer: 88.493% Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

102) A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of eighty eight weeks and a standard deviation of twenty five weeks. The next career begins on Monday; what is the likelihood that it endures for less than a year and a half? Answer: 34.46% Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

103) What are the differences between deterministic and probabilistic techniques? Answer: Deterministic techniques assume that no uncertainty exists in the model parameters. Probabilistic techniques include uncertainty and assume that there can be more than one solution. Diff: 1 Page Ref: 512 Section Heading: Types of Probability Keywords: deterministic techniques AACSB: Application of knowledge

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Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a period of one month and assigned them to five different categories as shown in the table. Commute Length commute time <10 minutes 10 ≤ commute time < 20 minutes 20 ≤ commute time < 30 minutes 30 ≤ commute time < 40 minutes 40 ≤ commute time < 50 minutes

Number of Observations 1 2 4 9 4

104) What is the likelihood that the commute will take 30 minutes or longer? Answer: 13/20 = 65% Diff: 1 Page Ref: 517 Section Heading: Fundamentals of Probability Keywords: cumulative probability distribution AACSB: Analytical thinking

105) What is the cumulative probability for the three shortest commute categories? Answer: (1 + 2 + 4)/20 = 0.35 Diff: 1 Page Ref: 517 Section Heading: Fundamentals of Probability Keywords: cumulative probability distribution AACSB: Analytical thinking

106) What is the average commute time for HOV Lane? Answer: Taking the midpoints of each observation as the value of the random variable, we get .05 × 5 + .1 × 15 + .2 × 25 + .45 × 35 + .2 × 45 = 31.5 minutes Diff: 1 Page Ref: 525 Section Heading: Expected Value Keywords: expected value AACSB: Analytical thinking

107) Assume that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2. Find the probability that X is between 48 and 55. Answer: 0.8351 Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

108) A paint manufacturer's production process is normally distributed with a mean of 100,000 gallons and a standard deviation of 10,000 gallons. Management wants to create an incentive bonus for the production crew when the daily production exceeds the 94th percentile of the distribution. At what level of production should management pay the incentive bonus? Answer: z = 1.56, so the incentive level is 115,600 gallons. Diff: 3 Page Ref: 530 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

19 .

An online sweepstakes has the following payoffs and probabilities. Each person is limited to one entry.

109) The probability that someone wins any money is ________. Answer: 0.1166 Diff: 1 Page Ref: 517 Section Heading: Fundamentals of Probability Keywords: probability distribution AACSB: Analytical thinking

110) The probability of winning at least $1000 is ________. Answer: 0.0006 Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: probability distribution AACSB: Analytical thinking

111) ________ techniques assume that no uncertainty exists in model parameters. A) Probability B) Probabilistic C) Deterministic D) Distribution Answer: C Diff: 2 Page Ref: 512 Section Heading: Types of Probability Keywords: deterministic methods AACSB: Application of knowledge

112) ________ probability is an estimate based on personal belief, experience, or knowledge of a situation. A) Binomial B) Subjective C) Marginal D) Joint Answer: B Diff: 2 Page Ref: 513 Section Heading: Types of Probability Keywords: subjective probability AACSB: Application of knowledge

20 .

113) Objective probabilities that can be stated prior to the occurrence of an event are: A) deterministic or probabilistic. B) subjective or objective. C) classical or a priori. D) relative or subjective. Answer: C Diff: 2 Page Ref: 512 Section Heading: Types of Probability Keywords: classical (or a priori) probability AACSB: Application of knowledge

114) The events in an experiment are ________ if only one can occur at a time. A) mutually exclusive B) non-mutually exclusive C) mutually inclusive D) independent Answer: A Diff: 1 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: mutually exclusive events AACSB: Application of knowledge

115) In a given experiment the probabilities of mutually exclusive events sum to: A) 0. B) 0.5. C) 1. D) This cannot be answered without knowing the probability values of the events. Answer: C Diff: 1 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: mutually exclusive events AACSB: Application of knowledge

116) A ________ probability is the probability of a single event occurring. A) subjective B) binomial C) marginal D) joint Answer: C Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: marginal probability AACSB: Application of knowledge

21 .

117) A frequency distribution is an organization of ________ data about the events in an experiment. A) quantitative B) integer C) qualitative D) unknown Answer: A Diff: 1 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: frequency distribution AACSB: Application of knowledge

118) Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will be accepted at both universities? A) .65 B) .25 C) .20 D) .09 Answer: D Diff: 2 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: multiplication of probabilities AACSB: Analytical thinking

119) Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will not be accepted at either university? A) .30 B) .36 C) .44 D) .56 Answer: C Diff: 2 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: multiplication of probabilities AACSB: Analytical thinking

22 .

120) Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category. Male (M) Female (F) Job Administrative (AD) Salaried staff (SS) Hourly staff (HS)

110 30 60

10 50 40

If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration? A) .17 B) .67 C) .70 D) .73 Answer: C Diff: 2 Page Ref: 517 Section Heading: Fundamentals of Probability Keywords: not mutually exclusive events, addition rule AACSB: Analytical thinking

121) The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and because he found their gentle clucking to relax him as he worked on his laptop on his deck. Their movements around his yard gave meaning to the term random walk — you literally could not predict their location from one minute to the next. His collection of birds is neatly summarized in this table. Breed Rhode Island Red Buff Orpington Barred Rock Australorp Leghorn

Rooster 2 0 0 0 1

Hen 8 5 6 6 2

A Rhode Island Red just joined him up on the deck; what is the probability it is a rooster? A) 0.20 B) 0.30 C) 0.33 D) 0.37 Answer: A Diff: 1 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: probabilistic techniques AACSB: Analytical thinking

23 .

122) The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and because he found their gentle clucking to relax him as he worked on his laptop on his deck. Their movements around his yard gave meaning to the term random walk — you literally could not predict their location from one minute to the next. His collection of birds is neatly summarized in this table. Breed Rhode Island Red Buff Orpington Barred Rock Australorp Leghorn

Rooster 2 0 0 0 1

Hen 8 5 6 6 2

What is the probability that the next chicken that joins him up on the deck is a rooster? A) .05 B) .10 C) .33 D) .66 Answer: B Diff: 1 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: probabilistic techniques AACSB: Analytical thinking

123) The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and because he found their gentle clucking to relax him as he worked on his laptop on his deck. Their movements around his yard gave meaning to the term random walk — you literally could not predict their location from one minute to the next. His collection of birds is neatly summarized in this table. Breed Rhode Island Red Buff Orpington Barred Rock Australorp Leghorn

Rooster 2 0 0 0 1

Hen 8 5 6 6 2

A hen just joined him up on the deck; what is the probability it is an Australorp? A) 0.18 B) 0.20 C) 0.22 D) 0.24 Answer: C Diff: 1 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: probabilistic techniques AACSB: Analytical thinking

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124) The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and because he found their gentle clucking to relax him as he worked on his laptop on his deck. Their movements around his yard gave meaning to the term random walk — you literally could not predict their location from one minute to the next. His collection of birds is neatly summarized in this table. Breed Rhode Island Red Buff Orpington Barred Rock Australorp Leghorn

Rooster 2 0 0 0 1

Hen 8 5 6 6 2

A hen just joined him up on the deck; what is the probability it is a rooster? A) 0.33 B) 0.10 C) 0.03 D) 0.00 Answer: D Diff: 1 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: probabilistic techniques AACSB: Analytical thinking

125) The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and because he found their gentle clucking to relax him as he worked on his laptop on his deck. Their movements around his yard gave meaning to the term random walk — you literally could not predict their location from one minute to the next. His collection of birds is neatly summarized in this table. Breed Rhode Island Red Buff Orpington Barred Rock Australorp Leghorn

Rooster 2 0 0 0 1

Hen 8 5 6 6 2

The farmer just spotted all of his Barred Rocks clustered together in the chicken run. Behind him, he hears a chicken creeping up on him, ready to pounce. What is the likelihood it is a Rhode Island Red rooster? A) 0.083 B) 0.100 C) 0.066 D) 0.166 Answer: A Diff: 1 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: probabilistic techniques AACSB: Analytical thinking

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126) A ________ probability distribution indicates the probability of r successes in n trials. A) joint B) subjective C) marginal D) binomial Answer: D Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial probability distribution AACSB: Application of knowledge

127) The probability of independent events occurring in succession is computed by ________ the probabilities of each event. A) multiplying B) adding C) subtracting D) dividing Answer: A Diff: 2 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: independent events AACSB: Application of knowledge

128) A ________ probability is the probability that an event will occur given that another event has already occurred. A) subjective B) objective C) conditional D) binomial Answer: C Diff: 2 Page Ref: 517 Section Heading: Statistical Independence and Dependence Keywords: conditional probability AACSB: Application of knowledge

129) In Bayesian analysis, additional information is used to alter the ________ probability of the occurrence of an event. A) marginal B) conditional C) binomial D) revised Answer: A Diff: 2 Page Ref: 523 Section Heading: Statistical Independence and Dependence Keywords: marginal probability AACSB: Application of knowledge

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130) Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category. Male (M) Female (F) Job Administrative (AD) Salaried staff (SS) Hourly staff (HS)

110 30 60

10 50 40

If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member? A) .50 B) .60 C) .625 D) .70 Answer: C Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: conditional probability AACSB: Analytical thinking

131) A ________ probability is the altered marginal probability of an event based on additional information. A) posterior B) joint C) marginal D) conditional Answer: A Diff: 2 Page Ref: 523 Section Heading: Statistical Independence and Dependence Keywords: posterior (revised) probability AACSB: Application of knowledge

132) Mutually exclusive events are: A) events with identical probabilities. B) events that have no outcomes in common. C) events that have no effect on each other. D) events that are represented in a Venn diagram by two overlapping circles. Answer: B Diff: 2 Page Ref: 514 Section Heading: Fundamentals of Probability Keywords: mutually exclusive events AACSB: Application of knowledge

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133) Bayesian analysis involves a(n) ________ probability. A) a priori B) posterior C) joint D) relative frequency Answer: B Diff: 2 Page Ref: 523 Section Heading: Statistical Independence and Dependence Keywords: Bayesian analysis AACSB: Application of knowledge

134) In a ________ distribution, for each of n trials, the event always has the same probability of occurring. A) binomial B) joint C) frequency D) standard Answer: A Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Application of knowledge

135) Experiments with repeated independent trials will be described by the binomial distribution if: A) each trial result influences the next. B) each trial has exactly two outcomes whose probabilities do not change. C) the trials are continuous. D) the time between trials is constant. Answer: B Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Application of knowledge

136) In a binomial distribution, for each of n trials, the event: A) time between trials is constant. B) always has the same probability of occurring. C) result of the first trial influence the next trial. D) trials are continuous. Answer: B Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Application of knowledge

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137) A fair die is rolled nine times. What is the probability that an odd number (1, 3, or 5) will occur less than 3 times? A) .0899 B) .2544 C) .7456 D) .9101 Answer: A Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

138) A fair die is rolled 8 times. What is the probability that an even number (2, 4, or 6) will occur between 2 and 4 times? A) .2188 B) .4922 C) .6016 D) .8204 Answer: C Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

139) It was a house with seven cats, four female and three male, and the litterbox was busier than O'Hare Airport during the week of Thanksgiving. The beleaguered husband's home office was right around the corner from the laundry room, where the litterbox was kept, and heard three separate instances of use. What is the likelihood that none of the instances were the work of the male cats? A) .273 B) .187 C) .429 D) .079 Answer: B Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

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140) It was a house with seven cats, four female and three male, and the litterbox was busier than O'Hare Airport during the week of Thanksgiving. The beleaguered husband's home office was right around the corner from the laundry room, where the litterbox was kept, and heard three separate instances of use. What is the likelihood that exactly one of the instances was the dutiful work of one the male cats? A) .273 B) .187 C) .419 D) .079 Answer: C Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

141) It was a house with seven cats, four female and three male, and the litterbox was busier than O'Hare Airport during the week of Thanksgiving. The beleaguered husband's home office was right around the corner from the laundry room, where the litterbox was kept, and heard three separate instances of use. What is the likelihood that exactly two of the instances were the dutiful work of the male cats? A) .273 B) .187 C) .429 D) .314 Answer: D Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

142) It was a house with seven cats, four female and three male, and the litterbox was busier than O'Hare Airport during the week of Thanksgiving. The beleaguered husband's home office was right around the corner from the laundry room, where the litterbox was kept, and heard three separate instances of use. What is the likelihood that all of the instances were the work of the male cats? A) .079 B) .187 C) .429 D) .314 Answer: A Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

30 .

143) It was a house with seven cats, four female and three male, and the litterbox was busier than O'Hare Airport during the week of Thanksgiving. The beleaguered husband's home office was right around the corner from the laundry room, where the litterbox was kept, and heard four separate instances of use. What is the likelihood that none of the instances were the work of the male cats? A) .273 B) .106 C) .034 D) .079 Answer: B Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

144) A company markets educational software products and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of "success" is 80%. Assume that the probability of success is independent for each product. What is the probability that exactly 1 of the 3 products is successful? A) 0.80 B) 0.032 C) 0.24 D) 0.096 Answer: D Diff: 2 Page Ref: 519 Section Heading: Statistical Independence and Dependence Keywords: binomial distribution AACSB: Analytical thinking

145) ________ is a measure of the dispersion of random variable values about the expected value or mean. A) Standard deviation B) Sample mean C) Population mean D) Expected value Answer: A Diff: 2 Page Ref: 524 Section Heading: Expected Value Keywords: variance, standard deviation AACSB: Application of knowledge

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146) An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as the table shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

p( )

.10

.15

.18

.20

.10

.07

What is the average number of complaints received per week? A) 2.12 B) 3.32 C) 4.12 D) 2.83 Answer: D Diff: 2 Page Ref: 525 Section Heading: Expected Value Keywords: expected value AACSB: Analytical thinking

147) The expected value of the standard normal distribution is equal to: A) 0 B) 1 C) 1.5 D) 2 Answer: A Diff: 1 Page Ref: 528 Section Heading: Expected Value Keywords: expected value AACSB: Application of knowledge

148) The area under the normal curve represents probability, and the total area under the curve sums to: A) 0 B) 0.5 C) 1 D) 2 Answer: C Diff: 2 Page Ref: 526 Section Heading: Expected Value Keywords: normal distribution AACSB: Application of knowledge

32 .

149) The ________ and variance are derived from a subset of the population data and are used to make inferences about the population. A) population variance B) population standard deviation C) population mean D) sample mean Answer: D Diff: 1 Page Ref: 520 Section Heading: Expected Value Keywords: mean and variance AACSB: Application of knowledge

150) Under the normal curve, the area between z = 1 and z = -2 includes approximately ________ of the values. A) 98% B) 95% C) 85% D) 82% Answer: D Diff: 3 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

151) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations? A) 84% B) 90% C) 95% D) 97% Answer: C Diff: 1 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

152) The weight of a jar of jelly is normally distributed with a mean of 16 oz and a standard deviation of 0.02 oz. What is the probability that a jar of jelly contains less than 16 oz? A) .1915 B) .3085 C) .5000 D) .7257 Answer: C Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

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153) The weight of a jar of jelly is normally distributed with a mean of 16 oz and a standard deviation of 0.02 oz. What is the probability that a jar of jelly contains more than 16.03 oz? A) .0668 B) .1587 C) .4332 D) .9332 Answer: A Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

154) Under the normal curve, the area between z = 2 and z = -2 includes ________ of the values. A) 98% B) 96% C) 95% D) 93% Answer: C Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

155) A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of eighty-eight weeks and a standard deviation of ten weeks. The next career begins on Monday; what is the likelihood that it endures for more than two years? A) 8.5% B) 7.5% C) 6.5% D) 5.5% Answer: D Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

34 .

156) A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of eighty-eight weeks and a standard deviation of twenty weeks. The next career begins on Monday; what is the likelihood that it endures for more than one year? A) 92% B) 94% C) 96% D) 98% Answer: C Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

157) A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of eighty-eight weeks and a standard deviation of twenty weeks. The next career begins on Monday; what is the likelihood that it endures for more than two years? A) 25% B) 21% C) 15% D) 11% Answer: B Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

158) A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of sixty six weeks and a standard deviation of twenty weeks. The next career begins on Monday; what is the likelihood that it endures for more than one year? A) 76% B) 66% C) 34% D) 24% Answer: A Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

35 .

159) A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of sixty six weeks and a standard deviation of ten weeks. The next career begins on Monday; what is the likelihood that it endures for less than one year? A) 14% B) 12% C) 10% D) 8% Answer: D Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

160) A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of sixty six weeks and a standard deviation of ten weeks. The next career begins on Monday; what is the likelihood that it endures for less than a year and a half? A) 82% B) 85% C) 88% D) 91% Answer: C Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

161) The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? A) 0.0228 B) 0.0475 C) 0.0485 D) 0.0500 Answer: B Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

36 .

162) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.2910. The value of Z is: A) 0.17. B) 0.81. C) 1.25. D) 1.65. Answer: B Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

163) For some value of Z, the probability that a standard normal variable is below Z is 0.3783. The value of Z is: A) -0.81. B) -0.31. C) 0.82. D) 1.55. Answer: B Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: standard normal distribution AACSB: Analytical thinking

164) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3554. The value of Z is: A) 0.31. B) 0.36. C) 0.95. D) 1.06. Answer: D Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

165) If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. A) 0.3551 B) 0.3085 C) 0.2674 D) 0.1915 Answer: B Diff: 1 Page Ref: 529 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

37 .

166) Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot. A) 0.1950 B) 0.4772 C) 0.4332 D) 0.6247 Answer: D Diff: 1 Page Ref: 529 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

167) Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot? A) 3.65 minutes B) 5.75 minutes C) 6.36 minutes D) 9.21 minutes Answer: A Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: normal distribution AACSB: Analytical thinking

168) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. What weight is exceeded by 2% of all of the crabs? (Assume the weights are normally distributed.) A) 0.78 pounds B) 1.82 pounds C) 2.42 pounds D) 4.36 pounds Answer: C Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

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169) A professor would like to assign grades such that 5% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.) A) 80 B) 83 C) 90 D) 93 Answer: B Diff: 2 Page Ref: 529 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

170) A professor would like to assign grades such that 7% of students receive Fs. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an F? (Round your answer.) A) 43 B) 49 C) 50 D) 55 Answer: A Diff: 2 Page Ref: 528 Section Heading: Expected Value Keywords: norm distrib, probability calculations with normal distribution AACSB: Analytical thinking

Number of Observations 1 2 4 9 4

171) What is the duration of Mr. Lane's expected commute? A) 31.5 minutes B) 27.25 minutes C) 25.5 minutes D) 33.75 minutes Answer: A Diff: 2 Page Ref: 525 Section Heading: Expected Value Keywords: expected value AACSB: Analytical thinking

39 .

172) What is the probability that Mr. Lane makes it home in under thirty minutes? A) .15 B) .35 C) .20 D) .55 Answer: B Diff: 2 Page Ref: 516 Section Heading: Fundamentals of Probability Keywords: cumulative probability distribution AACSB: Analytical thinking

173) What kind of probability is demonstrated if Mr. Lane is asked to predict the duration of his next commute? A) subjective probability B) conjecture probability C) objective probability D) reflexive probability Answer: C Diff: 2 Page Ref: 512 Section Heading: Types of Probability Keywords: objective probabilities, classical probabilities AACSB: Application of knowledge

174) Which of these events are mutually exclusive? A) The duration of Mr. Lane's commute is less than expected; Mr. Lane's commute is between twenty and thirty minutes. B) Mr. Lane's commute is longer than 30 minutes; Mr. Lane's commute is longer than 40 minutes. C) Mr Lanes commute is between ten and forty minutes; Mr. Lane's commute is between twenty and thirty minutes. D) Mr. Lane's commute takes less than ten minutes; Mr Lane's commute exceeds his expected commute. Answer: D Diff: 1 Page Ref: 515 Section Heading: Fundamentals of Probability Keywords: mutually exclusive events AACSB: Application of knowledge

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Introduction to Management Science, 12e (Taylor) Chapter 12 Decision Analysis 1) A state of nature is an actual event that may occur in the future. Answer: TRUE Diff: 1 Page Ref: 547 Section Heading: Components of Decision Making Keywords: state of nature AACSB: Application of knowledge

2) A payoff table is a means of organizing a decision situation, including the payoffs from different decisions given the various states of nature. Answer: TRUE Diff: 1 Page Ref: 547 Section Heading: Components of Decision Making Keywords: payoff table AACSB: Application of knowledge

3) The maximax criterion results in the maximum of the maximum payoffs. Answer: TRUE Diff: 2 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Application of knowledge

4) The maximin approach involves choosing the alternative with the highest payoff. Answer: FALSE Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge

5) Regret is the difference between the payoff from the best decision and all other decision payoffs. Answer: TRUE Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge

6) The minimax regret criterion minimizes the maximum regret. Answer: TRUE Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge

1 .

7) The minimax regret criterion maximizes the minimum regret. Answer: FALSE Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge

8) The Hurwicz criterion is a compromise between the maximax and maximin criteria. Answer: TRUE Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

9) The Hurwicz criterion is a compromise between the minimax and minimin criteria. Answer: FALSE Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

10) The coefficient of optimism is a measure of the decision maker's optimism. Answer: TRUE Diff: 1 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

11) The Hurwicz criterion multiplies the best payoff by the coefficient of optimism. Answer: TRUE Diff: 1 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

12) The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism. Answer: FALSE Diff: 1 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

13) A dominant decision is one that has a better payoff than another decision under each state of nature. Answer: TRUE Diff: 1 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: dominant decision AACSB: Application of knowledge

2 .

14) The appropriate criterion is dependent on the risk personality and philosophy of the decision maker. Answer: TRUE Diff: 3 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: decision making criteria AACSB: Application of knowledge

15) The maximax criterion is optimistic. Answer: TRUE Diff: 3 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: decision making criteria AACSB: Application of knowledge

16) The maximin criterion maximizes the minimum regret. Answer: FALSE Diff: 1 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge

17) The minimax criterion minimizes the maximum payoff. Answer: FALSE Diff: 1 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax criterion AACSB: Application of knowledge

18) Regret and opportunity loss mean the same thing. Answer: TRUE Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Application of knowledge

19) The equal likelihood criterion assigns a probability of 0.5 to each state of nature. Answer: FALSE Diff: 1 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Application of knowledge

20) Expected opportunity loss is the expected value of the regret for each decision. Answer: TRUE Diff: 2 Page Ref: 556 Section Heading: Decision Making with Probabilities Keywords: expected opportunity loss, minimax regret criterion AACSB: Application of knowledge

3 .

21) When using decision trees, branches with the greatest expected value are selected. Answer: TRUE Diff: 1 Page Ref: 561 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Application of knowledge

22) A decision tree is a diagram consisting of circular decision nodes, square probability nodes, and branches. Answer: FALSE Diff: 1 Page Ref: 561 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Application of knowledge

23) Additional information is used to alter the marginal probability of occurrence of an event in Bayesian analysis. Answer: TRUE Diff: 1 Page Ref: 570 Section Heading: Decision Analysis with Additional Information Keywords: Bayesian analysis AACSB: Application of knowledge

24) A conditional probability is the probability that two events will occur simultaneously. Answer: FALSE Diff: 1 Page Ref: 570 Section Heading: Decision Analysis with Additional Information Keywords: conditional probability AACSB: Application of knowledge

25) A posterior probability is the likelihood that an event has occurred after the decision maker has reached a decision. Answer: FALSE Diff: 1 Page Ref: 571 Section Heading: Decision Analysis with Additional Information Keywords: posterior (revised) probability AACSB: Application of knowledge

26) Events are mutually exclusive if one, and only one, can occur at a time. Answer: TRUE Diff: 1 Page Ref: 572 Section Heading: Decision Analysis with Additional Information Keywords: mutually exclusive events AACSB: Application of knowledge

4 .

27) The expected value of perfect information divided by the expected value of sample information is the efficiency of perfect information. Answer: FALSE Diff: 1 Page Ref: 576 Section Heading: Decision Analysis with Additional Information Keywords: efficiency of sample information AACSB: Analytical thinking

28) When the ________ criterion is used, the maximum of the maximum payoffs is selected. Answer: maximax Diff: 1 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: decision making without probabilities maximax criterion AACSB: Application of knowledge

29) When the ________ criterion is used, the maximum of the minimum payoffs is selected. Answer: maximin Diff: 1 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: decision making without probabilities, minimax criterion AACSB: Application of knowledge

30) ________ is the difference between the payoff from the best decision and all other decision payoffs. Answer: Regret Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: regret, minimax regret criterion AACSB: Application of knowledge

31) The ________ is a compromise between the maximax and the maximin criterion. Answer: Hurwicz criterion Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

32) The ________ is a measure of the decision makers optimism. Answer: coefficient of optimism Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: coefficient of optimism AACSB: Application of knowledge

33) A(n) ________ decision is one that has a better payoff than another decision under each state of nature. Answer: dominant Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: dominant decision AACSB: Application of knowledge

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34) A ________ structures decisions with a series of nodes. Answer: decision tree Diff: 1 Page Ref: 559 Section Heading: Decision Making without Probabilities Keywords: decision trees AACSB: Application of knowledge

35) The ________ of sample information is the ratio of the expected value of sample information to the expected value of perfect information. Answer: efficiency Diff: 1 Page Ref: 576 Section Heading: Decision Analysis with Additional Information Keywords: expected value of sample information AACSB: Application of knowledge

36) When the ________ criterion is used, the decision maker selects the decision alternative that minimizes the maximum regret. Answer: minimax regret Diff: 1 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax criterion AACSB: Application of knowledge

37) A ________ decision tree illustrates a situation requiring a series of decisions. Answer: sequential Diff: 1 Page Ref: 565 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Application of knowledge

38) ________ is a measure of personal satisfaction derived from money. Answer: Utility Diff: 1 Page Ref: 577 Section Heading: Utility Keywords: utility AACSB: Application of knowledge

39) People who forgo a high expected value to avoid a disaster with a low probability are ________. Answer: risk averters -or- risk averse Diff: 1 Page Ref: 577 Section Heading: Decision Making with Probabilities Keywords: risk averters, utility AACSB: Application of knowledge

40) The efficiency of sample information is the ratio of the expected value of sample information to ________. Answer: the expected value of perfect information Diff: 1 Page Ref: 576 Section Heading: Decision Analysis with Additional Information Keywords: expected value of perfect information AACSB: Analytical thinking

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41) The difference in the expected value with additional information and without additional information is ________. Answer: the expected value of sample information Diff: 1 Page Ref: 575 Section Heading: Decision Analysis with Additional Information Keywords: expected value of sample information AACSB: Analytical thinking

42) The efficiency of sample information multiplied by the expected value of perfect information is ________. Answer: the expected value of sample information Diff: 1 Page Ref: 576 Section Heading: Decision Analysis with Additional Information Keywords: expected value of sample information AACSB: Analytical thinking

43) If only one of three events can occur at any given time, the events are ________. Answer: mutually exclusive Diff: 1 Page Ref: 572 Section Heading: Decision Analysis with Additional Information Keywords: mutually exclusive events AACSB: Application of knowledge

44) If the decision maker receives additional information such that the marginal probabilities of certain events should be modified, these revised probabilities are called ________. Answer: posterior probabilities Diff: 1 Page Ref: 571 Section Heading: Decision Analysis with Additional Information Keywords: posterior (revised) probability AACSB: Application of knowledge

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A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Cold S1

Weather Warm Rainy S2 S3

Bike:

Hike:

Fish:

45) If the group is optimistic, what decision should they make? Answer: A2 Diff: 3 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

46) If the group is conservative, what decision will they make? Answer: A3 Diff: 3 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

47) If the group chooses to minimize their maximum regret, what activity will they choose? Answer: 3-way tie Diff: 3 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

48) If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected value criterion? Answer: Ev(a1) = 7.6 Ev(a2) = 9.6 (best) Ev(a3) = 8.2 Diff: 3 Page Ref: 555 Section Heading: Decision Making with Probabilities Keywords: expected value criterion AACSB: Analytical thinking

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49) If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively, then what is the EVPI for this situation? Answer: EVPI = 12.4 - 9.6 = 2.8 Diff: 3 Page Ref: 558 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking

An investor is consider four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

Investment

Poor (S1)

A B C D

50 80 -100 25

Economic Condition Average Good (S2) (S3) 75 15 300 25

Excellent (S4)

20 40 -50 25

30 50 10 25

50) What decision would be made under maximax? Answer: Compare 75, 80, 300, and 25. Choose investment C. Diff: 3 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

51) What decision would be made under maximin? Answer: Compare 20, 15, -100, and 25. Choose investment D. Diff: 3 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

52) What decision would be made under minimax regret? Answer: Compare 225, 285, 180, and 275. Select investment C. Diff: 3 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

53) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what investment would be made using the expected value criterion? Answer: Investment B with an EMV of 58. Diff: 3 Page Ref: 555 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking

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54) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what is the expected value of perfect information? Answer: The EVPI is 28.5. Diff: 3 Page Ref: 558 Section Heading: Decision Making without Probabilities Keywords: expected value criterion AACSB: Analytical thinking

A manager has developed a payoff table that indicates the profits associated with a set of alternatives under two possible states of nature. Alt

1 2 3

10 -2 8

2 8 5

55) If the manager uses maximin as the decision criterion, which of the alternatives should she choose? Answer: maximin: Alt 3 Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

56) If the manager uses minimax regret as the decision criterion, which of the alternatives would she choose? Answer: Select alternative 3. Alt

worst

1 2 3

0 12 2

6 0 3

6 12 3

(min regret)

Diff: 2 Page Ref: 540 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

57) Use the expected value criterion to select the best alternative. Assume that the probability of S2 is equal to 0.4. Answer: EV (Alt 1) = 0.6(10) + 0.4(2) = 6.8 EV (Alt 2) = 0.6(-2) + 0.4(8) = 2.0 EV (Alt 3) = 0.6(8) + 0.4(5) = 6.8 Select either alternative 1 or 3. Diff: 2 Page Ref: 555 Section Heading: Decision Making without Probabilities Keywords: expected value criterion AACSB: Analytical thinking

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58) Compute the expected value of perfect information assuming that the probability of S2 is equal to 0.4. Answer: EVPI = 0.6(10) + 0.4(8) - 6.8 = 2.4 Diff: 2 Page Ref: 558 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code.

59) If he uses the maximin criterion, how many new workers will he hire? Answer: 1 Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

60) If he uses the minimax regret criterion, how many new workers will he hire? Answer: 2 Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

61) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what are the expected net revenues for the number of workers he will decide to hire? Answer: $50,000 Diff: 2 Page Ref: 556 Section Heading: Decision Making with Probabilities Keywords: expected value criterion AACSB: Analytical thinking

62) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what is the expected value of perfect information? Answer: $26,000 Diff: 2 Page Ref: 558 Section Heading: Decision Making with Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking

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A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small plant is built, and demand is high, the production manager may choose to maintain the current size or to expand. The net present value of profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and a 50% chance the estimated net present value of profits will be $210,000. If a small facility is built and demand is low, there is no reason to expand and the net present value of the profits is $200,000. However, if a large facility is built and the demand turns out to be low, the choice is to do nothing with a net present value of $40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest, the net present value of the profits is $20,000. However, if the response to advertising is favorable, then the net present value of the profits is $220,000. Finally, if the large plant is built and the demand happens to be high, the net present value of the profits $800,000. 63) Draw a decision tree. Answer:

Diff: 2 Page Ref: 565 Section Heading: Decision Making with Probabilities Keywords: sequential decision tree AACSB: Analytical thinking

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64) Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the manufacturer choose? Answer:

EV1 = (.3)(20,000) + (.7)((220,000) = $160,000 EV2 = (.5)(330,000) + (.5)((210,000) = $270,000 EV3 = (.4)(200,000) + (.6)((270,000) = $242,000 EV4 = (.4)(160,000) + (.6)((800,000) = $544,000 Since 544,000 > 242,000, build a large plant. Diff: 3 Page Ref: 565 Section Heading: Decision Making with Probabilities Keywords: sequential decision tree AACSB: Analytical thinking

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65) If a student attends every management science class, the probability of passing the course is 0.80; but if the student only attends randomly, then the probability of passing the course is 0.50. If a student fails, he or she can take a makeup exam where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup exam drops to 0.10 if the student has attended at random. Passing the course is worth 5 credits. Full time attendance "costs" 3 credits in terms of energy and time, whereas random attendance "costs" only 1 credit. Use a decision tree to decide which is the best attendance pattern to adopt. Assume that all failing students take the make up exam and that the payoff for failing is equal to 0. Answer:

The expected value of attending all classes is 4.6 - 3 = 1.6. The expected value of attending randomly is 2.75 - 1 = 1.75, so the student should attend at random. Diff: 2 Page Ref: 549 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Analytical thinking

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The quality control manager for ENTA Inc. must decide whether to accept (A 1), further analyze (A2), or reject (A3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (S 1), 50 % chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S 3).

66) What action would you choose according to maximax criterion? Answer: (90 > 80 > 70), accept the lot, A 1. Diff: 2 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

67) What action would you choose according to maximin criterion? Answer: (10 < 20 < 40), reject the lot, A 3. Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

68) Construct the regret table. Answer: Regret Table

Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax criterion, regret table AACSB: Analytical thinking

69) What action would you choose according to minimax regret criterion? Answer: Regret Table

(80 > 60 > 50), therefore, reject the lot. Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax criterion AACSB: Analytical thinking

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70) What action would you choose according to expected value criterion? Answer: EV1 = (.3)(20) + (.5)(30) + (.2)(90) = 39 EV2 = (.3)(60) + (.5)(70) + (.2)(10) = 55 EV3 = (.3)(80) + (.5)(50) + (.2)(40) = 57 Since 57 > 55 > 39, reject the lot. Diff: 2 Page Ref: 556 Section Heading: Decision Making with Probabilities Keywords: expected value criterion AACSB: Analytical thinking

71) What is the maximum amount that you would be willing to pay for perfect information? Answer: Expected payoff with perfect information = (.3)(80) + (.5)(70) + (.2)(90) = 77 EVPI = 77 - max (EV) = 77 -57 = 20 Diff: 3 Page Ref: 558 Section Heading: Decision Making with Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking

72) Lucky Lucy is playing the slots in Reno, Nevada, holding her last silver dollar. There are three possible payoffs if she wins: one cherry, $1; two cherries, $5; or three cherries, $50. Anything else on the slot machine loses. Construct the payoff table for Lucky Lucy. Answer:

Diff: 2 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: payoff table AACSB: Analytical thinking

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Cold & Calculating The cold, calculating father did exactly that when examining the 27 year old failure to launch man child that had turned his walk in closet into a bedroom. As he saw it, there were five alternatives; each had its advantages and disadvantages, and under different circumstances, each had a different financial incentive. He laid it all out neatly in a table, but as not to arouse suspicion, he left the table's labels very generic, so the alternatives were simply labeled A through E while the different circumstances were simply numbered one through three. He flicked the gray ash off of his favorite purple smoking jacket and pondered the best course of action under each possible future. It was good to be devious, he decided.

A B C D E

One 19 26 24 43 36

Two 6 5 18 34 34

Three 20 48 17 15 15

73) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an apertif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. "Wait a minute Hurwicz, that figure sounds as if I'm afraid of making a decision," the father intoned. "It seems that depending on how optimistic I am, the optimal choice changes between alternative B and alternative D. Furthermore, another transition point exists between alternatives C and D. What is this devilry, Hurwicz?" Help Leonid Hurwicz identify the range of coefficients of optimism that render alternatives, B, C, and D superior to all others. Answer: A coefficient of optimism from 0 up to 0.096 would make alternative C most attractive. A coefficient of optimism from 0.096 up to 0.666 would make alternative D most attractive. A coefficient of optimism beyond 0.666 would make alternative B most attractive. Diff: 3 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking

74) The cold, calculating father had little reason for optimism and tended towards a pessimistic view of the entire world. Still, it might be useful to see what the other half thinks, he thought to himself. Identify the optimal alternatives under these two opposite views of the world. Answer: The optimistic view of the world would suggest alternative B by virtue of its score of 48 in state of nature 3. The pessimistic view of things would select alternative C thanks to its lusty 17 under alternative 3. Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

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75) "Cletus, my boy," he said to his dog that was dozing peacefully before the fireplace, "I don't like to look back on my decisions with any regret. In fact, in my golden years I make most of my decisions so that when I do look back, I have as little regret as possible." What is the regret table and optimal choice given this state of mind? Answer: The regret table looks something like this:

A B C D E

1 24 17 19 0 7

2 28 29 16 0 0

3 28 0 31 33 33

The minimum of the maximum regrets is the 28 associated with alternative A in state of nature 3. Diff: 3 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars. School Vanderbilt Texas Tech Seattle Northeastern State

Scenario 1 95 55 90 65

Scenario 2 20 60 10 50

Scenario 3 -10 60 80 60

76) Kip tends to be extremely optimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why? Answer: Maximax is the optimistic criterion, which would result in the selection of Vanderbilt as it has the best of the best payoffs among all alternatives. Diff: 2 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

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77) Pedro is extremely pessimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why? Answer: Maximin is the pessimist's criterion. This would result in the selection of Texas Tech University by virtue of its $55,000 payoff being higher than all other alternatives' worst outcomes. Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

78) Napoleon doesn't know what to think, since he has no idea which scenario will happen. Which criterion is he well-suited for and what is his decision? Answer: Napoleon is an equally-likely decision maker in this example, so he would opt for Seattle University and its $60,000 per year average. Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking

79) Summer bursts into the meeting and announces that there's another way to consider the issue. Since Napoleon will have to live with his choice for the rest of his life, he might consider selecting the alternative that will cause him the least pain in hindsight when he compares his outcome with what he might have gained. Which criterion is she talking about, what is the best school for this criterion, and why? Answer: This is the minimax regret criterion. Northeastern State University is the MBA of choice under this criterion with a maximum regret of only $30,000 per year. Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

80) Napoleon's Uncle Rico believes that the scenarios are not necessarily equally likely, and suggests that the likelihood of occurrence of Scenario 2 is 0.4 and the likelihood of occurrence of Scenarios 1 and 3 are both 0.3. What two criteria are most appropriate and what is the resulting decision? Answer: The two criteria are expected monetary value and expected opportunity loss. The EMV is highest for Texas Tech University at $58,500 and the EOL is the lowest for Texas Tech University at $18,000. Diff: 2 Page Ref: 556 Section Heading: Decision Making with Probabilities Keywords: expected opportunity loss AACSB: Analytical thinking

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The Vacation Final exams are almost here and once they are done, it will be time to reward myself with a well-deserved vacation. As a state employee, I haven't seen a raise since... well, ever. Thus an important criterion, in fact the most important criterion is to find an exotic region that can be visited inexpensively. There are three states of nature that could impact costs in these five areas of interest, and they correspond to the relative strength of the US Dollar against that region's dominant currency. Rather than squander my time doing any actual publishable research, instead I have determined the average cost per day to visit each region under each of the possible states of nature. This table, which should not be construed as actual vacation advice, appears below. Region

Strong Dollar

Eastern Europe Southeast Asia Australia Galapagos Islands Scandinavia

33 41 45 37 38

Middling Dollar 54 56 44 35 11

Weak Dollar 57 36 58 26 48

81) My wife always looks on the bright side of life. Where would she recommend we travel and why? Answer: Maximax is the optimistic criterion when we consider profits, but these are costs, so an optimist would adopt the minimin criterion as most appropriate. The lowest of the lowest costs is $32 per day associated with Scandinavia. Hei suomi! Diff: 2 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: minimin criterion AACSB: Analytical thinking

82) I'm a pessimistic person, perhaps it has to do with the twenty years in my chosen profession. Where should I recommend we travel and why? Answer: Maximin is the pessimistic criterion when we consider profits, but these are costs, so an pessimist would adopt the minimax criterion as most appropriate. The lowest of the highest costs is $38 per day associated with the Galapagos Islands. Hola Galapagos! Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimin criterion AACSB: Analytical thinking

83) I spend a lot of time second guessing myself and would hate to look back in a year or two and realize that I had spent more than I needed to. Where should I recommend we travel and why? Answer: This mindset screams for a minimax regret criterion. The lowest of the location regrets is the $4 associated with the Galapagos Islands. Hola Galapagos! Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

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84) I spend a lot of time second guessing myself and would hate to look back in a year or two and realize that I had spent more than I needed to. What does the regret table look like for this decision and what is the location of choice? Answer: This mindset screams for a minimax regret criterion. The regret table is: Eastern Europe Southeast Asia Australia Galapagos Scandinavia

Strong $ 0 8 12 4 5

Middling $ 22 24 12 3 0

Weak $ 21 0 22 2 12

The lowest of the location maximum regrets is the $4 associated with the Galapagos Islands. Hola Galapagos! Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

85) I have absolutely no clue what will happen with the strength of the dollar and can't imagine assigning likelihoods or adopting an optimistic or pessimistic stance. What's the safest bet for a destination and why? Answer: This mindset screams for an equally likely criterion. The lowest of the location averages is the $36.66 associated with the Galapagos Islands. Hola Galapagos! Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking

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86) Consider the following decision tree.

What is the expected value at node 4? Answer: $600 Diff: 1 Page Ref: 565 Section Heading: Decision Making with Probabilities Keywords: expected value, decision trees AACSB: Analytical thinking

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87) Consider the following decision tree.

What is the value associated with node 3? Answer: $2,500 Diff: 2 Page Ref: 565 Section Heading: Decision Making without Probabilities Keywords: expected value, decision trees AACSB: Analytical thinking

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88) Consider the following decision tree.

Which decision, A or B, is best? What is the expected value of this decision? Answer: A, expected payoff = $2,100 Diff: 2 Page Ref: 566 Section Heading: Decision Making with Probabilities Keywords: expected value, decision trees AACSB: Analytical thinking

89) The maximax criterion results in the: A) maximum of the minimum payoffs. B) maximum of the maximum payoffs. C) minimum of the maximum payoffs. D) minimum of the minimum payoffs. Answer: B Diff: 1 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Application of knowledge

90) The maximin criterion results in the: A) minimum of the maximum payoffs. B) maximum of the maximum payoffs. C) maximum of the minimum payoffs. D) minimum of the minimum payoffs. Answer: C Diff: 1 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge

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91) Regret is the difference between the payoff from the: A) best decision and all other decision payoffs. B) worst decision and all other decision payoffs. C) best decision and the worst decision payoffs. D) none of the above Answer: A Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: regret, minimax regret criterion AACSB: Application of knowledge

92) The ________ minimizes the maximum regret. A) maximax regret criterion B) minimax regret criterion C) minimin regret criterion D) maximin regret criterion Answer: B Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge

93) The minimax regret criterion: A) maximizes the minimum regret. B) minimizes the minimum regret. C) minimizes the maximum regret. D) maximizes the maximum regret. Answer: C Diff: 1 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge

94) Determining the worst payoff for each alternative and choosing the alternative with the best worst is called: A) maximin. B) minimin. C) maximax. D) minimax. Answer: A Diff: 1 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge

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95) The maximin approach to decision making refers to: A) minimizing the maximum return. B) maximizing the minimum return. C) maximizing the maximum return. D) minimizing the minimum return. Answer: B Diff: 1 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge

96) The term opportunity loss is most closely related to: A) maximin regret. B) maximax regret. C) minimax regret. D) minimin regret. Answer: C Diff: 2 Page Ref: 540 Section Heading: Decision Making without Probabilities Keywords: expected opportunity loss, minimax regret criterion AACSB: Application of knowledge

97) The Hurwicz criterion is a compromise: A) between the maximin and minimax criteria. B) between the minimax and maximax criteria. C) between the maximax and maximin criteria. D) none of the above Answer: C Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

98) The Hurwicz criterion multiplies the: A) best payoff by the coefficient of optimism. B) worst payoff by the coefficient of optimism. C) best payoff by the worst payoff. D) none of the above Answer: A Diff: 1 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

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99) The basic decision environment categories are: A) certainty. B) risk. C) uncertainty. D) all of the above Answer: D Diff: 2 Page Ref: 547 Section Heading: Decision Making without Probabilities Keywords: decision making AACSB: Application of knowledge

Scenario 1 95 55 90 65

Scenario 2 20 60 10 50

Scenario 3 -10 60 80 60

100) Under which decision making criterion is Vanderbilt University the optimal choice? A) maximax B) maximin C) minimax regret D) equally likely Answer: A Diff: 2 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

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101) Under which decision making criterion is Texas Tech University the optimal decision? A) maximax B) maximin C) minimax regret D) equally likely Answer: B Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

102) Under which criterion is Seattle University the optimal decision? A) maximax B) maximin C) minimax regret D) equally likely Answer: D Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking

103) Under which criterion is Northeastern State University the optimal decision? A) maximax B) maximin C) minimax regret D) equally likely Answer: C Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

104) Suppose that the likelihood for each of the scenarios 1 through 3 is 0.3, 0.4, and 0.3, respectively. What is the optimal decision under the expected opportunity loss criterion? A) Vanderbilt University B) Texas Tech University C) Seattle University D) Northeastern State University Answer: B Diff: 2 Page Ref: 556 Section Heading: Decision Making with Probabilities Keywords: expected opportunity loss AACSB: Analytical thinking

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Strong Dollar

Eastern Europe Southeast Asia Australia Galapagos Islands Scandinavia

33 41 45 37 38

Middling Dollar 54 56 44 35 11

Weak Dollar 57 36 58 26 48

105) An optimistic vacationer would opt for: A) Scandinavia. B) Galapagos Islands. C) Australia. D) Eastern Europe. Answer: A Diff: 2 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: minimin criterion AACSB: Analytical thinking

106) An pessimistic vacationer would opt for: A) Scandinavia. B) Galapagos Islands. C) Australia. D) Eastern Europe. Answer: B Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax criterion AACSB: Analytical thinking

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107) After staring blankly at the options for several hours, the family decides they truly have no idea which value of the dollar would be more likely and overall feel neither optimistic nor pessimistic. What's the safest choice for them to make? A) Scandinavia B) Australia C) Galapagos Islands D) Eastern Europe Answer: C Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking

108) What do the regrets look like for Scandinavia from left to right? A) 0, 21, 24 B) 0, 15, 5 C) 6, 0, 16 D) 5, 0, 12 Answer: D Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: minimax criterion, regret table AACSB: Analytical thinking

109) What is the vacation of choice under the minimax regret criterion? A) Galapagos Islands B) Eastern Europe C) Southeast Asia D) Australia Answer: A Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: minimax criterion, regret table AACSB: Analytical thinking

110) What does the coefficient of optimism need to exceed in order for the Galapagos Islands to not be the vacation destination of choice? A) 0.80 B) 0.77 C) 0.74 D) 0.71 Answer: B Diff: 3 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking

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A B C D E

One 19 26 24 43 36

Two 6 5 18 34 34

Three 20 48 17 15 15

111) It was tough to be optimistic, but the cold, calculating father did exactly that, inspired by a particularly smooth single malt scotch. Which alternative would be the best choice given this rare state of optimism? A) A B) B C) C D) D Answer: B Diff: 2 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

112) The father had built his fortune as a real estate speculator and now devoted his energies to his new passion, pessimism. Which alternative would be the best choice given this new hobby? A) A B) B C) C D) D Answer: C Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

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113) "Regrets? I've had a few," and his voice trailed off. He was speaking to no one in particular, which he found himself doing with alarming frequency. If at all possible, he made decisions that would allow him to look back with as little regret as possible. Which alternative would be the best choice given this proclivity for minimizing regret? A) A B) B C) C D) D Answer: A Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking

114) He set the analysis aside for a few days and when he noticed it on his drawing table he studied it. He vaguely remembered the potential courses of action but couldn't for the life of himself remember what the different states of nature were. "This is certainly embarrassing," he muttered. Perhaps it didn't really matter as long as he treated each state of nature as equally likely. They certainly were in his own mind now that he couldn't remember what they were. "If that's not the definition of equally likely, I don't know what is," he commented to his faithful manservant Jeeves. Which alternative would be the best choice given this predicament? A) A B) B C) C D) D Answer: D Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking

115) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an apertif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. What is the optimal choice for him? A) A B) B C) C D) D Answer: D Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking

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116) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an apertif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.7. What is the optimal choice for him? A) A B) B C) C D) D Answer: B Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking

117) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an apertif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. "Wait a minute Hurwicz, that figure sounds as if I'm afraid of making a decision," the father intoned. "It seems that depending on how optimistic I am, the optimal choice changes between alternative B and alternative D." What coefficient of optimism would make the cold, calculating father indifferent between these two alternatives? A) 0.583 B) 0.616 C) 0.666 D) 0.714 Answer: C Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking

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118) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an apertif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. "Wait a minute Hurwicz, that figure sounds as if I'm afraid of making a decision," the father intoned. "It seems that depending on how optimistic I am, the optimal choice changes between alternative C and alternative D." What coefficient of optimism would make the cold, calculating father indifferent between these two alternatives? A) 0.096 B) 0.125 C) 0.167 D) 0.183 Answer: A Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking

119) The basic decision environment categories are: A) certainty and risk. B) risk and uncertainty. C) certainty and uncertainty. D) certainty, uncertainty and risk. Answer: D Diff: 2 Page Ref: 547 Section Heading: Decision Making without Probabilities Keywords: decision making AACSB: Application of knowledge

120) The Hurwicz criterion: A) multiplies the worst payoff by one minus the coefficient of optimism. B) multiplies the best payoff by one minus the coefficient of optimism. C) is a compromise between the minimax and maximin criteria. D) all of the above Answer: A Diff: 1 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge

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121) The appropriate criterion is dependent on: A) the risk personality of the decision maker. B) the number of nodes in the decision tree. C) the magnitude of the payoffs. D) none of the above Answer: A Diff: 3 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: decision making AACSB: Application of knowledge

122) The ________ is a measure of the decision maker's optimism. A) equal likelihood criterion B) dominant decision C) coefficient of optimism D) opportunity loss Answer: C Diff: 2 Page Ref: 551 Section Heading: Decision Making without Probabilities Keywords: coefficient of optimism, Hurwicz criterion AACSB: Application of knowledge

123) The ________ multiplies the decision payoff for each state of nature by an equal weight. A) dominant decision B) coefficient of optimism C) equal likelihood criterion D) none of the above Answer: C Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Application of knowledge

124) A ________ is one that has a better payoff than another decision under each state of nature. A) coefficient of optimism B) equal likelihood criterion C) dominant decision D) none of the above Answer: C Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: dominant decision AACSB: Application of knowledge

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125) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The maximax strategy is: A) Buy. B) Rent. C) Lease. D) Brisk. Answer: A Diff: 1 Page Ref: 549 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking

126) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The maximin strategy is: A) Buy. B) Rent. C) Lease. D) Brisk. Answer: C Diff: 2 Page Ref: 550 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking

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127) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The equal likelihood criterion strategy is: A) Buy. B) Rent. C) Lease. D) Brisk. Answer: C Diff: 2 Page Ref: 552 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking

128) A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is: A) 12. B) 55. C) 57. D) 69. Answer: A Diff: 2 Page Ref: 558 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking

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129) The ________ is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence. A) expected value B) expected value of perfect information C) expected opportunity loss D) none of the above Answer: A Diff: 2 Page Ref: 555 Section Heading: Decision Making with Probabilities Keywords: expected value AACSB: Application of knowledge

130) The ________ is the expected value of the regret for each decision. A) expected value B) expected opportunity loss C) expected value of perfect information D) none of the above Answer: B Diff: 2 Page Ref: 556 Section Heading: Decision Making with Probabilities Keywords: expected opportunity loss AACSB: Application of knowledge

131) A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a: A) decision tree. B) payoff table. C) feasible region. D) payback matrix. Answer: B Diff: 2 Page Ref: 547 Section Heading: Components of Decision Making Keywords: payoff table AACSB: Application of knowledge

132) The ________ is the maximum amount a decision maker would pay for additional information. A) expected opportunity loss B) expected value C) expected value of perfect information D) bid price Answer: C Diff: 2 Page Ref: 558 Section Heading: Decision Making with Probabilities Keywords: expected value of perfect information AACSB: Application of knowledge

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133) A decision tree is a diagram consisting of: A) branch angles that vary as likelihoods increase. B) triangle probability nodes. C) branches representing decision alternatives. D) perfect information. Answer: C Diff: 1 Page Ref: 549 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Application of knowledge

134) In ________ additional information is used to alter the marginal probability of the occurrence of an event. A) Bayesian analysis B) decision analysis C) probability analysis D) decision making under certainty Answer: A Diff: 2 Page Ref: 570 Section Heading: Decision Analysis with Additional Information Keywords: Bayesian analysis AACSB: Application of knowledge

135) A ________ probability is the probability that an event will occur given that another event has already occurred. A) posterior B) conditional C) marginal D) low Answer: B Diff: 2 Page Ref: 570 Section Heading: Decision Analysis with Additional Information Keywords: conditional AACSB: Application of knowledge

136) A ________ probability is the altered marginal probability of an event based on additional information. A) marginal B) conditional C) posterior D) none of the above Answer: C Diff: 2 Page Ref: 571 Section Heading: Decision Analysis with Additional Information Keywords: posterior AACSB: Application of knowledge

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137) The efficiency of sample information is the ratio of the expected value of sample information to the: A) expected value of perfect information. B) expected value. C) utilization rate. D) coefficient of optimism. Answer: A Diff: 2 Page Ref: 576 Section Heading: Decision Analysis with Additional Information Keywords: efficiency of sample information AACSB: Application of knowledge

138) The expected value of sample information: A) is never more than EVPI. B) can be greater or less than EVPI. C) can be positive or negative. D) is equivalent to the EVPI. Answer: A Diff: 2 Page Ref: 575 Section Heading: Utility Keywords: efficiency of sample information AACSB: Application of knowledge

139) People who forgo a high expected value to avoid a disaster with a low probability are: A) risk takers. B) risk averters. C) risk calculators. D) risk predictors. Answer: B Diff: 1 Page Ref: 577 Section Heading: Utility Keywords: risk averters, utility AACSB: Application of knowledge

140) People who take a chance on a bonanza with a very low probability of occurrence in lieu of a sure thing are: A) risk takers. B) risk averters. C) risk calculators. D) risk predictors. Answer: A Diff: 1 Page Ref: 577 Section Heading: Utility Keywords: risk takers, utility AACSB: Application of knowledge

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141) Utiles are units of ________ measures of utility. A) quantitative B) objective C) subjective D) qualitative Answer: C Diff: 3 Page Ref: 567 Section Heading: Utility Keywords: utility AACSB: Application of knowledge

A small entrepreneurial company is trying to decide between developing two different products that they believe they can sell to two potential companies, one large and one small. If they develop Product A, they have a 50% chance of selling it to the large company with annual purchases of about 20,000 units. If the large company won't purchase it, then they think they have an 80% chance of placing it with a smaller company, with sales of 15,000 units. On the other hand if they develop Product B, they feel they have a 40% chance of selling it to the large company, resulting in annual sales of about 17,000 units. If the large company doesn't buy it, they have a 50% chance of selling it to the small company with sales of 20,000 units. 142) What is the probability that Product A will being purchased by the smaller company? A) 0.8 B) 0.5 C) 0.4 D) 0.2 Answer: C Diff: 2 Page Ref: 561 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Analytical thinking

143) What is the probability that Product B will being purchased by the smaller company? A) 0.8 B) 0.5 C) 0.4 D) 0.3 Answer: D Diff: 2 Page Ref: 559 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Analytical thinking

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144) How many units of Product A can they expect to sell? A) 20,000 B) 17,000 C) 16,000 D) 15,000 Answer: C Diff: 2 Page Ref: 559 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 13 Queuing Analysis 1) Providing quick service is an important aspect of quality customer service. Answer: TRUE Diff: 1 Page Ref: 608 Section Heading: Elements of Waiting Line Analysis Keywords: waiting lines AACSB: Application of knowledge

2) Operating characteristics describe the methods used by the service process. Answer: FALSE Diff: 2 Page Ref: 608 Section Heading: Elements of Waiting Line Analysis Keywords: operating characteristics AACSB: Application of knowledge

3) Waiting lines form because people or things arrive at the servicing function, or server, faster than they can be served. Answer: TRUE Diff: 1 Page Ref: 608 Section Heading: Elements of Waiting Line Analysis Keywords: waiting lines AACSB: Application of knowledge

4) Components of a waiting line system include arrivals, servers, and the calling population. Answer: FALSE Diff: 1 Page Ref: 609 Section Heading: The Single-Server Waiting Line System Keywords: components of a waiting line AACSB: Application of knowledge

5) The most important factors to consider in analyzing a queuing system are queuing discipline, arrival and service rate, and the nature of the calling population. Answer: TRUE Diff: 3 Page Ref: 609 Section Heading: The Single-Server Waiting Line System Keywords: queuing system AACSB: Application of knowledge

6) The queue discipline is the order in which waiting customers are served. Answer: TRUE Diff: 1 Page Ref: 609 Section Heading: The Single-Server Waiting Line System Keywords: queuing discipline AACSB: Application of knowledge

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7) The calling population is the source of customers. Answer: TRUE Diff: 1 Page Ref: 609 Section Heading: The Single-Server Waiting Line System Keywords: calling population AACSB: Application of knowledge

8) Calling populations are always finite. Answer: FALSE Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: calling population AACSB: Application of knowledge

9) The arrival rate is the frequency at which customers arrive at a waiting line according to a probability distribution. Answer: TRUE Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: arrival rate AACSB: Application of knowledge

10) The arrival rate is most frequently described by a negative exponential distribution. Answer: FALSE Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: arrival rate, Poisson distribution AACSB: Application of knowledge

11) The service rate is the average time it takes to serve a customer. Answer: FALSE Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: service rate, exponential distribution AACSB: Application of knowledge

12) The service time can often be described by the Poisson distribution. Answer: FALSE Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: service rate, negative exponential distribution AACSB: Application of knowledge

13) Queuing system operating statistics are constant over time. Answer: TRUE Diff: 2 Page Ref: 613 Section Heading: The Single-Server Waiting Line System Keywords: queuing system, steady state AACSB: Application of knowledge

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14) As the level of service improves, the cost of service decreases. Answer: FALSE Diff: 1 Page Ref: 616 Section Heading: The Single-Server Waiting Line System Keywords: service level AACSB: Application of knowledge

15) Queue discipline describes customers' behavior in the queue. Answer: FALSE Diff: 1 Page Ref: 610 Section Heading: Queuing Keywords: queuing discipline AACSB: Application of knowledge

16) The basic single-server queuing model assumes an infinite calling population. Answer: TRUE Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: queuing, calling population AACSB: Application of knowledge

17) Utilization of 100% is necessary for a queuing system to reach a steady state. Answer: FALSE Diff: 1 Page Ref: 613 Section Heading: The Single-Server Waiting Line System Keywords: queuing systems, utilization AACSB: Application of knowledge

18) Queuing models provide optimal solutions to waiting line problems. Answer: FALSE Diff: 1 Page Ref: 608 Section Heading: The Single-Server Waiting Line System Keywords: queuing models, operating characteristics AACSB: Application of knowledge

19) All single-server queuing models require the utilization factor to be less than 1. Answer: TRUE Diff: 1 Page Ref: 613 Section Heading: The Single-Server Waiting Line System Keywords: queuing system utilization AACSB: Application of knowledge

20) Queue discipline refers to the willingness of customers to wait in line for service. Answer: FALSE Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: queuing discipline AACSB: Application of knowledge

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21) The basic single-server model assumes that arrival rates are normally distributed. Answer: FALSE Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting line syst, utilization rate, idle percent AACSB: Application of knowledge

22) A car wash with two attendants who work together as a team would be an example of a multipleserver system. Answer: FALSE Diff: 2 Page Ref: 627 Section Heading: The Multiple-Server Waiting Line Keywords: single-server queuing model AACSB: Application of knowledge

23) In multiple-server models, two or more servers work as a team to serve a single waiting line. Answer: FALSE Diff: 2 Page Ref: 627 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Application of knowledge

24) In a multiple-server system, the ratio of the mean effective service rate for the system to the arrival rate to the system must be greater than 1 for customers to be served in a reasonable time. Answer: TRUE Diff: 1 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Application of knowledge

25) The multiple-server system models have been developed on the assumption that the service times are normally distributed. Answer: FALSE Diff: 1 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: service rate, exponential distribution AACSB: Application of knowledge

26) The number of servers, c, in a multiple-server queuing system must be greater than the average queue length. Answer: FALSE Diff: 1 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multi server waiting line, expected avg num of customers in sys AACSB: Application of knowledge

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27) Server utilization in a multiple-server system is calculated the same as in a single-server system. Answer: FALSE Diff: 1 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: utilization AACSB: Analytical thinking

28) In real-world queuing applications, the multiple-server system analysis techniques are the same whether customers wait in one line or in separate lines due to customer balking. Answer: FALSE Diff: 1 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple channel waiting line system, number of servers AACSB: Application of knowledge

29) In systems with finite queue length, the service rate does not have to exceed the arrival rate. Answer: TRUE Diff: 2 Page Ref: 621 Section Heading: Finite Calling Population Keywords: queuing system, finite queue length AACSB: Application of knowledge

30) The basic single-server model assumes that customers who arrive first are served first. Answer: TRUE Diff: 2 Page Ref: 610 Section Heading: Queuing Keywords: queuing discipline AACSB: Application of knowledge

31) If it takes 5 minutes to serve a customer at a fast food restaurant the service rate is ________. Answer: 12 customers per hour Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting line system, mean arrival rate AACSB: Analytical thinking

32) The ________ is the average number of customers who can be served during a given time period. Answer: service rate Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: service rate AACSB: Application of knowledge

33) The service time can most often be described by the ________ distribution. Answer: negative exponential Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: service time, negative exponential distribution AACSB: Application of knowledge

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34) The ________ is the frequency at which the customers arrive at a waiting line according to a probability distribution. Answer: arrival rate Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: arrival rate AACSB: Application of knowledge

35) The arrival rate can generally be described by a(n) ________ distribution. Answer: Poisson Diff: 2 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: arrival rate, Poisson distribution AACSB: Application of knowledge

36) The ________ is the source of the customers or objects being simulated. Answer: calling population Diff: 2 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: calling population AACSB: Application of knowledge

37) A system has one service facility that can service 10 customers per hour. The customers arrive at an average rate of 6 per hour. Utilization is ________. Answer: 60% Diff: 2 Page Ref: 613 Section Heading: The Single-Server Waiting Line System Keywords: utilization AACSB: Analytical thinking

38) A situation in which a mechanic is responsible for repairing a pool of fleet vehicles should be analyzed for a waiting line system with a ________ calling population. Answer: finite Diff: 1 Page Ref: 614 Section Heading: Finite Calling Population Keywords: single server waiting line system, arrival rate AACSB: Application of knowledge

39) Customers arrive at a candy shop every 8 minutes on average. The arrival rate is ________. Answer: 7.5 customers per hour Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting line system, arrival rate AACSB: Analytical thinking

40) If λ = 24 and μ = 30, then utilization is equal to ________. Answer: 80% Diff: 1 Page Ref: 613 Section Heading: Queuing Keywords: single server waiting model, utilization AACSB: Analytical thinking

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41) In a single-server system, if λ = 24 and μ = 30, then L is equal to ________. Answer: 4 customers Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model, avg wait time AACSB: Analytical thinking

42) In a single-server system, if λ = 24 and μ = 30, then W is equal to ________ minutes. Answer: 10 Diff: 2 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model, avg wait time AACSB: Analytical thinking

43) In the ________ queuing system, which is a variation of the single-phase single-channel model, the service rate does not have to exceed the arrival rate. Answer: finite Diff: 2 Page Ref: 624 Section Heading: Finite Calling Population Keywords: finite queue length AACSB: Application of knowledge

44) ________ is the act of a customer refusing to enter a service system because the wait is too lengthy. Answer: Balking Diff: 2 Page Ref: 632 Section Heading: Additional Types of Queuing Systems Keywords: balking, reneging AACSB: Application of knowledge

45) Movement by customers between two or more queues in a system is called ________. Answer: jockeying Diff: 2 Page Ref: 633 Section Heading: Additional Types of Queuing Systems Keywords: jockeying AACSB: Application of knowledge

46) As customers move through a processing center line they first wait in the reception room, then they fill in some personal information on a tablet PC once one becomes available. Finally, they head to another waiting area before submitting a sample. This queuing system is ________. Answer: multiple-servers in sequence Diff: 2 Page Ref: 632 Section Heading: Additional Types of Queuing Systems Keywords: multiple-server waiting line AACSB: Application of knowledge

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47) The number of servers multiplied by the service rate is the ________ for a multiple-server system. Answer: mean effective service rate Diff: 2 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

48) A single-channel queuing system has an average service time of 10 minutes and an average time between arrivals of 15 minutes. What is the arrival rate? Answer: 4 per hour Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting line system, arrival rate AACSB: Analytical thinking

49) In a single-server queuing system, if 10 customers arrive per hour, and 20 customers are served per hour, what is the probability that there are no customers in the system? Answer: 0.5 Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting line syst, utilization rate, idle percent AACSB: Analytical thinking

50) A single-bay car wash with a Poisson arrival rate and an exponential service time has cars arriving an average of 15 minutes apart. It takes approximately 9 minutes to wash a car. What is the system utilization? Answer: 0.60 Diff: 1 Page Ref: 613 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting line sys, utilization rate, sys utilization AACSB: Analytical thinking

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. 51) What is the utilization rate for the mechanic? Answer: 57% Diff: 1 Page Ref: 613 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting model, utilization AACSB: Analytical thinking

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52) What is the average time that a snowplow is out of service? Answer: .33 day or 2.64 hours Diff: 2 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

53) On average, how long does a snowplow wait before the mechanic can begin his repair? Answer: 0.19 day or 1.52 hours Diff: 2 Page Ref: 613 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

54) Approximately how many vehicles are in the garage, waiting for repairs or being repaired? Answer: 1.33 plows Diff: 2 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

55) Poultry Processing processes chickens for fast food restaurants. The Majestic chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processed within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. Determine the maximum average processing rate (in truckloads per hour) that must be designed for the machine, in order to ensure that the cages will be processed, on the average, in 30 minutes or less. Assume processing time is exponentially distributed. Answer: μ = 10 trucks per hour Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting model, service rate AACSB: Analytical thinking

Lenny, a graduate research assistant "moonlights" at the short order counter in the student union snack bar in the evenings. He is the only one on duty at the counter during the hours he works. Arrivals to the counter seem to follow the Poisson distribution with a mean of 8 per hour. Each customer is served one at a time and the service time follows an exponential distribution with a mean of 5 minutes. 56) How long will a student wait in line, on average? Answer: 0.167 hour or 10 minutes Diff: 1 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting model, utilization AACSB: Analytical thinking

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57) The manager thinks that students will go elsewhere for lunch if they have to wait more than 5 minutes. Therefore he's thinking of hiring another server to help Lenny, reducing the customer service time to 4 minutes. How long will students wait in line if Lenny gets help? Answer: .01 hour or 0.31 minutes Diff: 2 Page Ref: 628 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting model, queue length AACSB: Analytical thinking

58) Instead of having another student help Lenny, the manager is thinking of having two lines instead. Customers will equally divide themselves between the two lines. How long will students wait in line if there's a second server? (Assume that the service time is 5 minutes.) Answer: The arrival rate will be cut in half but the service rate remains the same. Waiting time in line is .04 hours or 2.5 minutes or 150 seconds. Diff: 3 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: probability of full system, finite queue length AACSB: Analytical thinking

At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals. 59) On average how many people are waiting in line at any time and what is the average wait? Answer: Average queue length = 0.24 customer; Average wait = 0.59 minute = 0.01 hour Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: queuing system AACSB: Analytical thinking

60) On average, how busy are the servers and how likely is it that they have nothing to do? Answer: The servers are busy half (0.50) of the time and there is a 0.21 probability that the system is completely empty. Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: utilization AACSB: Analytical thinking

61) What is the likelihood that there are three or fewer customers in the entire system? How does this compare with the likelihood of three or fewer customers in a system with the same arrival and service rates but staffed by four servers? Answer: The likelihood of 0, 1, 2, and 3 customers is 0.21, 0.32, 0.24, and 0.12, respectively, for a total of 0.88 for the three or fewer customers with three servers. If the number of servers increases to four, then the likelihoods of 0, 1, 2, and 3 are .22, .33, .25, and .12, respectively, for a total of .93. Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: utilization AACSB: Analytical thinking

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62) On average, how many people are either waiting in line or currently being served? Answer: The average number of people in the entire system is 1.74; 0.24 of them are in line and 1.5 being served. Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: utilization AACSB: Analytical thinking

63) An aggressive advertising campaign increases demand for the service by 50%. By what percentage do the average queue length and average time in queue increase? Answer: The average queue length is now 1.7 customers and the average time in queue is now 0.05 hour or 2.84 minutes. Under the previous arrival rate, there were 0.24 customer in the system and a time in queue of 0.1 hour or 0.59 minute. The queue length has increased by 608% and the queue time has increased by 381%. Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: queuing system AACSB: Analytical thinking

64) A hotel is considering changing its waiting line system. In the current system, hotel guests divide themselves equally between the lines that form in front of 4 hotel clerks. The manager is considering having hotel guests wait in one line and then proceed to the next available clerk. If average service time is 10 minutes and the average number of arrivals per hour is 12 guests, determine which system results in the lowest customer waiting time. Answer: Current system: λ = 12/4 = 3. W = .333 hour or 20 minutes. Proposed system: W = .1812 or 10.8 minutes, so the proposed system results in less waiting time. Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple channel waiting line system, average waiting time AACSB: Analytical thinking

65) The local grocery store consists of two cashiers. The customers arrive according to a Poisson distribution and the service times are based on a negative exponential distribution. The average customer service time is 5 minutes and the average time between the arrivals of successive customers is 3 minutes. What is the probability that there are no customers in the grocery store? Answer: P0 = .0909 Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: probability no customers in sys, multi channel waiting line sys AACSB: Analytical thinking

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The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers. 66) What is the average number of customers waiting in each line and being checked out? Answer: L = 2 customers in system with 0.66 being checked out and 1.33 in the line Diff: 3 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: avg num of customers in the sys, multi channel waiting line sys AACSB: Analytical thinking

67) How much time is a customer expected to spend waiting in line and being checked out? Answer: Wq = .13 hour or 8 minutes and W = 0.2 hour or 12 minutes Diff: 3 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: avg time customer spends in sys, multi channel wait line sys AACSB: Analytical thinking

68) On average, how much time will the customer spend in line waiting to be served? Answer: Wq = .1333 hours or 8 minutes Diff: 3 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: avg time customer spends in queue, multi channel wait line sys AACSB: Analytical thinking

69) On average, how many customers are waiting in line to be served? Answer: Lq = 1.33 customers Diff: 3 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: avg num of customers in queue, multi channel waiting line sys AACSB: Analytical thinking

70) A multiple channel queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service time of 20 minutes per customer. What is the minimum number of servers required to avoid an overloaded system? Answer: 3 Diff: 2 Page Ref: 618628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple channel waiting line system, number of servers AACSB: Analytical thinking

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In a factory, machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution, but has a mean of 8 minutes and a standard deviation of 3 minutes. 71) What is the probability that no machine is being fixed? Answer: P0 = 1 - .8 = .2 Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: probability of no customers in sys, undef/constant service times AACSB: Analytical thinking

72) On average, how many machines are waiting in line to be fixed? Answer: Lq = 1.83 machines Diff: 3 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: avg num of custs waiting in line, undefined/constant service times AACSB: Analytical thinking

73) On average, how many machines are in the system either being repaired or waiting in line to be repaired? Answer: L = 2.63 machines Diff: 3 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: avg num of customers in the system, undefined and constant service times AACSB: Analytical thinking

74) On average, how long will a machine have to wait before it is fixed? Answer: Wq = 0.3 hour or 18.25 minutes Diff: 3 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: average time spent in queue, undefined/constant service times AACSB: Analytical thinking

75) On average, how long will a machine be down and out of service? Answer: W = 0.44 hour or 26.25 minutes Diff: 3 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: average time spent in system, undefined/constant service times AACSB: Analytical thinking

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In a bank drive-through, there is a single service window and room only for two cars to line-up to wait for service. The mean time between arrivals for drive through customers is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to a Poisson distribution and the service times are exponentially distributed. 76) What is the probability that there are no vehicles in the system? Answer: P0 = .46 Diff: 3 Page Ref: 624 Section Heading: Finite Queue Length Keywords: probability no customers in the system, finite queue length AACSB: Analytical thinking

77) On average, how many cars are in the system? Answer: L = 0.9 cars Diff: 3 Page Ref: 625 Section Heading: Finite Queue Length Keywords: number of customers in the system, finite queue length AACSB: Analytical thinking

78) What is the probability that the system is full and new arrival must drive on? Answer: PM = 0.1 Diff: 3 Page Ref: 624 Section Heading: Finite Queue Length Keywords: probability of full system, finite queue length AACSB: Analytical thinking

79) On average, how many customers are waiting to be served? Answer: Lq = .36 car Diff: 3 Page Ref: 624 Section Heading: Finite Queue Length Keywords: number of customers in the waiting line, finite queue length AACSB: Analytical thinking

80) What is the average time a customer spends in the system? Answer: W = 0.08 hour or 5.02 minutes Diff: 3 Page Ref: 625 Section Heading: Finite Queue Length Keywords: avg time customer spends in system, finite queue length AACSB: Analytical thinking

81) What is the average time a customer spends in the line waiting to be served? Answer: Wq = 0.03 hour or 2.02 minutes Diff: 3 Page Ref: 625 Section Heading: Finite Queue Length Keywords: avg time customer spends in waiting line, finite queue length AACSB: Analytical thinking

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82) Operating characteristics for a waiting line system include: A) queue discipline. B) the Poisson distribution. C) a waiting line structure. D) utilization. Answer: D Diff: 1 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting line system, components of a waiting line AACSB: Application of knowledge

83) An important factor to consider in analyzing a queuing system is the: A) queue discipline. B) queue structure. C) queue order. D) cost. Answer: A Diff: 3 Page Ref: 609 Section Heading: The Single-Server Waiting Line System Keywords: queuing system, queuing discipline AACSB: Application of knowledge

84) Customers may be served: A) according to a number assigned to each item. B) on a first-come-first-serve basis. C) on a last-come-first-serve basis. D) all of the above Answer: D Diff: 2 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: queuing system, queuing discipline AACSB: Application of knowledge

85) In a single-server queuing model, L represents the: A) length of time a customer waits. B) size of the queue. C) average number of customers waiting and being served. D) length of the line. Answer: C Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Application of knowledge

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86) Queuing system operating statistics: A) change from start to finish during the day. B) are constant over time. C) include queue discipline, arrival rate, and service rate. D) all of the above Answer: B Diff: 2 Page Ref: 613 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Application of knowledge

87) Queuing discipline refers to: A) the reason waiting occurs in underloaded systems. B) the willingness of customers to wait in line. C) the order in which customers are processed. D) how constant the interarrival times are. Answer: C Diff: 2 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: queuing discipline AACSB: Application of knowledge

88) The arrival rate is the: A) time between arrivals to the service facility. B) rate items arrive at the server after being in queue. C) rate of arrivals to the service facility. D) time a customer spends in line. Answer: C Diff: 2 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: arrival rate AACSB: Application of knowledge

89) A single-server queuing system has average time between arrivals of 20 minutes and a service time of 10 minutes each. Assuming Poisson arrivals and exponential service times, the utilization factor is approximately: A) 0.25. B) 0.33. C) 0.50. D) 2.0. Answer: C Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting model, utilization AACSB: Analytical thinking

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90) What happens to the customer waiting time if system utilization increases? A) decreases exponentially B) decreases proportionally C) increases proportionally D) increases exponentially Answer: D Diff: 2 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: system utilization, customer waiting time AACSB: Analytical thinking

91) What is not considered a measure of system performance in a queuing analysis? A) average number in the system B) system utilization C) average number waiting in line D) service time Answer: D Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: queuing analysis, system performance AACSB: Application of knowledge

92) Which of the following will not decrease system utilization? A) increase in arrival rate B) increase in service rate C) increase in the number of servers D) decrease in service time Answer: A Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: system utilization AACSB: Analytical thinking

A single-server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution. 93) The average time a customer can expect to wait in line is: A) 18 minutes. B) 36 minutes. C) 30 minutes. D) 60 minutes. Answer: A Diff: 2 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: average waiting time, single server waiting line AACSB: Analytical thinking

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94) The probability that the system is idle is: A) 0. B) .20. C) .40. D) .60. Answer: C Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: probability that system is idle, single server waiting line AACSB: Analytical thinking

95) The expected number of customers in the system is: A) 3.0. B) 1.5. C) 1.0. D) .90. Answer: B Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: number of customers in the system, single server waiting line AACSB: Analytical thinking

96) The expected number of customers in the waiting line is: A) .6. B) .7. C) .8. D) .9. Answer: D Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: number of customers in wait line, single server waiting line AACSB: Analytical thinking

97) A system has 5 servers. Customers arrive at a rate of 6 per hour and service time is 20 minutes. What is the system utilization? A) .83 B) .40 C) .50 D) 20 Answer: B Diff: 2 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

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A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. 98) The utilization is: A) .30. B) .45. C) .57. D) .85. Answer: C Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting model, utilization AACSB: Analytical thinking

99) Determine the average time that a snowplow is out of service. A) .33 hours B) 20 minutes C) 2.64 hours D) .19 days Answer: C Diff: 2 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: expected waiting time in the queue, single server waiting line sys AACSB: Analytical thinking

100) On average, how long does a plow wait before the mechanic begins the repair? A) 0.19 hour B) 1.25 hours C) 1.52 hours D) 2.64 hours Answer: C Diff: 2 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: expected num of customers in sys, single server waiting line sys AACSB: Analytical thinking

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101) What is the expected average number of snowplows in the garage (waiting for repair and being repaired)? A) 1 B) 1.33 C) 2 D) 2.52 Answer: B Diff: 3 Page Ref: 612 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

102) In a single-server queuing system, if 12 customers arrive per hour and 30 customers are served per hour, what is the probability that there are no customers in the system? A) 0.75 B) 0.60 C) 0.40 D) 0.2 5 Answer: B Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single server queuing sys, probability no customers in the sys AACSB: Analytical thinking

Jolt - Exp The soda machine outside the lecture hall sees a steady stream of customers throughout the day. While the machine takes 4 seconds to deliver a can of carbonated sugar water once the button is pressed, the student customers introduce variation into the delivery process by pondering their selection for a while. Thus, we can safely say that the service time is governed by a negative exponential probability distribution that averages 10 seconds. Over the course of a twelve hour lecture day, students arrive at the rate of 240 per hour, Poisson distributed of course. 103) On average, how many students are standing directly in front of the soda machine? A) 2 B) 1.33 C) 0.67 D) 0.5 Answer: A Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

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104) Over the course of the twelve hour day, how many hours is the soda machine not happily dispensing product? A) 2 B) 4 C) 6 D) 8 Answer: B Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting model, utilization AACSB: Analytical thinking

105) Nathan is cutting it close today. At 10:00:00 AM, the professor will close the door to the classroom and ignore any requests to enter the room once his scintillating lecture has begun. Nathan approaches the soda machine at 9:59:20. Will he make it to class on time? A) Nathan will be late by ten seconds. B) Nathan will be exactly on time. C) Nathan will be early by ten seconds. D) Nathan will be early by twenty seconds. Answer: C Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

106) Nathan is cutting it close today. At 10:00:00 AM, the professor will close the door to the classroom and ignore any requests to enter the room once his scintillating lecture has begun. What is the probability that he finds only one person at the machine buying a soda? A) 0.1 B) 0.15 C) 0.22 D) 0.33 Answer: C Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

107) At the end of an average twelve hour day, how many cans of soda will the vending machine have dispensed? A) 4320 B) 3600 C) 3240 D) 2880 Answer: D Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

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108) When the soda machine is not dispensing product, its CPU participates in the SETI project. It takes one second to examine an interstellar signal for signs of intelligence. Over the course of an entire 24 hour period, how many signals can the soda machine examine? A) 57,600 B) 43,200 C) 28,800 D) 14,400 Answer: A Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

109) Michelle is reviewing flash cards while in line waiting for her turn to buy a refreshing beverage. It takes two seconds to quiz herself on each flash card. If her wait today is an average wait, how many cards can she review before it's time to make that purchase? A) 20 B) 10 C) 5 D) 2 Answer: B Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

110) Tim is wary of large crowds and won't approach the soda machine if there are five or more people at the machine. What percentage of the time does Tim forego a soda due to the large crowd? A) 30% B) 20% C) 13% D) 9% Answer: C Diff: 3 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

111) What percentage of the time is there one person at the machine? A) 56% B) 44% C) 33% D) 22% Answer: D Diff: 3 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

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Jolt - K The soda machine outside the lecture hall sees a steady stream of customers throughout the day. The machine takes 4 seconds to deliver a can of carbonated sugar water once the button is pressed and students generally know what they want from the machine - the average feeding of the machine takes two seconds. Over the course of a twelve hour lecture day, students arrive at the rate of 500 per hour. 112) How long is the average wait at the soda machine? A) 15 seconds B) 20 seconds C) 25 seconds D) 30 seconds Answer: A Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Analytical thinking

113) Jake is cutting it close for class this morning. Right now it is 9:59:40 and the professor has been known to slam the door and lock it at 10:00:00, laughing manically at the students that are out in the hall. Jake desperately needs a soda to make it through class this morning so he stops to buy one. What will be the outcome of this decision? A) Jake will enjoy his soda out in the hall, having missed class by five seconds. B) Jake will enjoy his soda out in the hall, having missed class by one second. C) Jake will enjoy his soda while listening to a lecture having made it in the room with five seconds to spare. D) Jake will enjoy his soda while listening to a lecture having made it in the room with fourteen seconds to spare. Answer: B Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Analytical thinking

114) About how many people are waiting in line at the machine on average? A) 0 B) 1 C) 2 D) 3 Answer: C Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Analytical thinking

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115) What is the average number of folks either purchasing a soda or waiting to purchase one? A) 1.83 B) 2.16 C) 2.46 D) 2.92 Answer: D Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Analytical thinking

116) When idle, the soda machine's CPU is tasked with participating in the Enigma@home project. If it can try 5 different solutions per second, how many solutions can it propose over the course of a twelve hour day? A) 36,000 B) 30,000 C) 24,000 D) 18,000 Answer: A Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Analytical thinking

117) Josie likes to tweet almost as much as she enjoys an ice cold soda. If she can type at the rate of two characters per second, how many full tweets can she send out while waiting in line for a soda? Assume that Josie's tweets always completely fill the maximum number of twitter characters. A) Josie can send about a third of a tweet. B) Josie can send about a half a tweet. C) Josie can send about three-fourths of a tweet. D) Josie can send one tweet. Answer: B Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Analytical thinking

118) The soda delivery guy stocks up the machine at the start of each day. How many cans of soda will he need to stock up the machine each morning? A) 600 B) 720 C) 6,000 D) 7,200 Answer: C Diff: 1 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Analytical thinking

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119) How many minutes out of each hour is the soda machine not serving a customer? A) 16 B) 15 C) 12 D) 10 Answer: D Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Analytical thinking

120) A manager is trying to improve a single-server queueing system through automation. The average service time is 20 minutes per customer, exponentially distributed, and the arrival rate is 16 customers per 8-hour day (Poisson arrivals). The automated system will have a constant service time of 16 minutes. The effect of this change will: A) decrease utilization. B) increase waiting time. C) decrease waiting time. D) have no effect since the service time is unchanged. Answer: C Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Application of knowledge

121) A multiple-channel system has customers arriving at an average rate of 5 per hour and an average service time of 40 minutes. What minimum number of servers is required to ensure that the system is not overloaded? A) 4 B) 5 C) 6 D) 3 Answer: A Diff: 1 Page Ref: 619 Section Heading: The Single-Server Waiting Line System Keywords: multiple-server waiting line AACSB: Analytical thinking

122) A single-channel queuing system has an average service time of 8 minutes and an average time between arrivals of 10 minutes. What is the hourly arrival rate? A) 8 B) 6 C) 4 D) 2 Answer: B Diff: 1 Page Ref: 610 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting line, arrival rate AACSB: Analytical thinking

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123) A multiple-channel queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 4 customers per hour and an average service time of 18 minutes per customer. What is the minimum number of servers required to avoid an overloaded system? A) 1 B) 2 C) 3 D) 4 Answer: B Diff: 1 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: number of servers AACSB: Analytical thinking

124) Poultry Processing processes chickens for fast food restaurants. The chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processed within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. What is the minimum average processing rate (in truckloads per hour) that must be designed for the machine in order to ensure that the cages will be processed, on the average, in 30 minutes or less? Assume processing time is exponentially distributed. A) 4.5 trucks per hour B) 9 trucks per hour C) 10 trucks per hour D) 18 trucks per hour Answer: C Diff: 2 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single server waiting model, service rate AACSB: Analytical thinking

125) Constant service times occur with A) machinery. B) well-trained employees. C) service processes. D) assembly processes. Answer: A Diff: 2 Page Ref: 628 Section Heading: Undefined and Constant Service Times Keywords: constant service times AACSB: Application of knowledge

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126) Customers arrive at a music store at an average of 1 per minute (Poisson arrivals). The service rate is 15 customers per hour (exponential service times). What is the minimum number of servers needed to keep the waiting time in the system under 5 minutes? A) 4 B) 5 C) 6 D) 7 Answer: B Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple channel waiting line system, average waiting time AACSB: Analytical thinking

127) A single-bay car wash with a Poisson arrival rate and an exponential service time has cars arriving at an average of 10 minutes apart with an average service time of 4 minutes. What is the system utilization? A) 0.3 B) 0.4 C) 0.5 D) 0.6 Answer: B Diff: 1 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: system utilization AACSB: Analytical thinking

128) Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson distribution. The wash time is a constant 4 minutes. What is the average number of cars in line? A) .022 B) .133 C) .267 D) .667 Answer: B Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: constant service time, queue length AACSB: Analytical thinking

129) Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson distribution. The wash time averages 4 minutes with a standard deviation of 1 minute, but the wash time is not defined by any distribution. What is the average number of cars in line? A) .142 B) .267 C) .283 D) 2.83 Answer: A Diff: 2 Page Ref: 619 Section Heading: Undefined and Constant Service Times Keywords: undefined service time AACSB: Analytical thinking

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130) In a finite queue, the length of the queue is: A) limited. B) unlimited. C) limited or unlimited. D) limited and unlimited. Answer: A Diff: 2 Page Ref: 614624 Section Heading: Finite Calling Population Keywords: finite queue AACSB: Application of knowledge

131) Pickmeup is a drive through coffee house that has room for 3 cars in the driveway. The line cannot exceed 3 cars, and because they are exclusively drive through, customers may be turned away. In the morning, the arrival rate is 40 cars per hour (Poisson distributed) and with the servers working in teams, they can process 50 cars per hour (the service rate is exponential). What is the probability of turning customers away? A) .173 B) .210 C) .339 D) .410 Answer: A Diff: 3 Page Ref: 621 Section Heading: Finite Queue Length Keywords: probability of full system, finite queue length AACSB: Analytical thinking

132) In multiple-server models, ________ independent servers in parallel serve a single waiting line. A) 2 or more B) 3 or more C) 4 or more D) 5 or more Answer: A Diff: 1 Page Ref: 627 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Application of knowledge

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The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers. 133) How much time is a customer expected to spend waiting in line and checking out? A) 8 minutes B) 12 minutes C) 16 minutes D) 20 minutes Answer: B Diff: 3 Page Ref: 611 Section Heading: The Multiple-Server Waiting Line Keywords: single-server queuing model AACSB: Analytical thinking

134) On average, how much time will the customer spend in line waiting to be served? A) 8 minutes B) 12 minutes C) 16 minutes D) 20 minutes Answer: A Diff: 3 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model, avg wait time AACSB: Analytical thinking

135) What is the probability that there are no customers in the grocery store? A) .166 B) .333 C) .5 D) .667 Answer: B Diff: 3 Page Ref: 611 Section Heading: The Single-Server Waiting Line System Keywords: single-server queuing model AACSB: Analytical thinking

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At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals. 136) How busy are the servers on average? A) 50% utilized B) 60% utilized C) 70% utilized D) 80% utilized Answer: A Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: utilization AACSB: Analytical thinking

137) How many customers are either waiting or being served on average? A) 1.5 B) 1.74 C) 1.98 D) 2.22 Answer: B Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: queuing models, operating characteristics AACSB: Analytical thinking

138) What is the average time a customer spends in the system? A) 2.5 minutes B) 3.7 minutes C) 4.3 minutes D) 5.6 minutes Answer: C Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: queuing models, operating characteristics AACSB: Analytical thinking

139) What percentage of the time is the system completely empty? A) 9% B) 13% C) 17% D) 21% Answer: D Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: queuing models, operating characteristics AACSB: Analytical thinking

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140) What is the likelihood there are more than three customers in the system? A) 12% B) 24% C) 76% D) 88% Answer: A Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: queuing models, operating characteristics AACSB: Analytical thinking

Jolt - M The soda machines outside the lecture hall sees a steady stream of customers throughout the day. Between the student's use of the machine and the mechanism, it takes 15 seconds (exponentially distributed) to deliver a can of carbonated sugar water to a thirsty customer. Over the course of a twelve hour lecture day, students arrive at the rate of 450 per hour. 141) How many minutes out of each hour is the soda machine not serving a customer? A) 1.8 B) 2.2 C) 2.6 D) 3.0 Answer: A Diff: 2 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

142) About how many people are waiting in line for a soda? A) 11.8 B) 13.6 C) 15.5 D) 17.2 Answer: B Diff: 2 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

31 .

143) It is precisely two minutes before class begins when Lisa decides to buy a soda. The professor has a well-deserved reputation for locking out everyone that is even a second late. Undeterred, Lisa makes a beeline for the machines, their eerie glow and soothing hum calling to her almost as much as the promise of an ice cold beverage. "I'm pretty sure I can make it," she remarks to a classmate as she gets in line for a soda, "and if I'm late, all I need to do is bat my eyelashes at him and he'll open the door and even apologize for shutting it in the first place." What will be the result of Lisa's decision to purchase a soda before class? A) Lisa will easily make it to her seat with a refreshing soda, entering the room twenty seconds before class begins. B) Lisa will march into the lecture hall triumphantly holding her soda aloft a full twelve seconds before class begins. C) Lisa will need to start batting those eyelashes, because she's almost four seconds late for class. D) Lisa will need to shift those eyelashes into overdrive as she is more than fourteen seconds late for class. However, at least she has a soda. Answer: C Diff: 2 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

144) What is the likelihood that there aren't enough customers making purchases or waiting in line to form a barbershop quartet? A) 0.33 B) 0.30 C) 0.25 D) 0.20 Answer: D Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple server waiting line, barbershop quartet AACSB: Analytical thinking

145) How many times will you find more than twenty-one customers either buying a soda or waiting in line to make that purchase? A) one in four B) one in five C) one in six D) one in seven Answer: A Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

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146) The soda machines have become self aware and when they are not in use dispensing ice-cold beverages, they are busy formulating a plan for world domination. About how much time over the course of a week can they develop their battle plans? A) 84 hours B) 89 hours C) 94 hours D) 99 hours Answer: B Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

147) The local soda machines union has some concerns regarding how busy these two machines are during the day. The union has work rules that demand that machines can be no busier than working twothirds of their scheduled work shift. How many machines should they demand management add to the work force to bring them in line with the utilization rule? A) 3 machines B) 2 machines C) 1 machine D) none - they are already at that figure Answer: C Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

148) The local soda machines union has some concerns regarding how busy these two machines are. They have work rules that demand that machines can be no busier than working half of their scheduled work shift. How many machines should be employed to bring them in line with the utilization rule? A) 1 machine B) 2 machines C) 3 machines D) 4 machines Answer: D Diff: 3 Page Ref: 628 Section Heading: The Multiple-Server Waiting Line Keywords: multiple-server waiting line AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 14 Simulation 1) In computer mathematical simulation, a system is replicated with a mathematical model that is analyzed with the computer. Answer: TRUE Diff: 1 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: computer mathematical simulation AACSB: Application of knowledge

2) Monte Carlo is a technique for selecting numbers randomly from a probability distribution. Answer: TRUE Diff: 1 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

3) The Monte Carlo process is analogous to gambling devices. Answer: TRUE Diff: 2 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

4) In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution. Answer: TRUE Diff: 2 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

5) A long period of real time can be represented by a short period of simulated time. Answer: TRUE Diff: 1 Page Ref: 649 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation, simulated time AACSB: Application of knowledge

6) Random numbers are equally likely to occur. Answer: TRUE Diff: 1 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Application of knowledge

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7) Simulation results will always equal analytical results if 30 trials of the simulation have been conducted. Answer: FALSE Diff: 2 Page Ref: 652 Section Heading: The Monte Carlo Process Keywords: steady state AACSB: Application of knowledge

8) It's often difficult to validate that the results of a simulation truly replicate reality. Answer: TRUE Diff: 1 Page Ref: 652 Section Heading: The Monte Carlo Process Keywords: simulation results AACSB: Application of knowledge

9) Simulation applies mathematical models to determine optimal solutions to business problems. Answer: FALSE Diff: 2 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: simulations AACSB: Application of knowledge

10) Validation of a simulation model occurs when the true steady state average results have been reached. Answer: TRUE Diff: 1 Page Ref: 653 Section Heading: The Monte Carlo Process Keywords: simulations, computer simulation AACSB: Application of knowledge

11) Random numbers generated by a mathematical process instead of a physical process are pseudorandom numbers. Answer: TRUE Diff: 2 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: random numbers AACSB: Application of knowledge

12) Random numbers are typically generated on the computer using a numerical technique. Answer: TRUE Diff: 2 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: random numbers AACSB: Application of knowledge

13) A table of random numbers must be normally distributed and efficiently generated. Answer: FALSE Diff: 2 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: random numbers AACSB: Application of knowledge

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14) When using Excel to simulate a system, it is necessary to compute only the probability (relative frequency) distribution. Answer: FALSE Diff: 2 Page Ref: 654 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: simulation with Excel AACSB: Application of knowledge

15) Excel can only be used to simulate systems that can be represented by continuous random variables. Answer: FALSE Diff: 2 Page Ref: 654 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: simulation with Excel AACSB: Application of knowledge

16) In Excel the VLOOKUP function is used to determine values for continuous random variables. Answer: FALSE Diff: 2 Page Ref: 655 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: simulation with Excel AACSB: Application of knowledge

17) Developing the cumulative probability distribution helps to determine random number ranges. Answer: TRUE Diff: 2 Page Ref: 659 Section Heading: Simulation of a Queuing System Keywords: cumulative probability distribution AACSB: Analytical thinking

18) Starting conditions have no impact on the validity of a simulation model. Answer: FALSE Diff: 2 Page Ref: 660 Section Heading: Simulation of a Queuing System Keywords: simulation results, starting conditions AACSB: Application of knowledge

19) Simulations should always be started with an empty system. Answer: FALSE Diff: 2 Page Ref: 676 Section Heading: Verification of the Simulation Model Keywords: simulation results AACSB: Application of knowledge

20) Manual simulation is limited because of the amount of real time required to simulate even one trial. Answer: TRUE Diff: 3 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: manual simulation AACSB: Application of knowledge

3 .

21) Applications of simulation models reflecting continuous distributions are more common than those of models employing discrete distributions. Answer: TRUE Diff: 1 Page Ref: 662 Section Heading: Continuous Probability Distributions Keywords: continuous random variables AACSB: Application of knowledge

22) In a continuous probability function, the area under the curve represents the probability of occurrence of the random variable. Answer: TRUE Diff: 2 Page Ref: 662 Section Heading: Continuous Probability Distributions Keywords: continuous random variables AACSB: Application of knowledge

23) Cumulative probabilities are analogous to the discrete ranges of random numbers used in the Monte Carlo process. Answer: TRUE Diff: 2 Page Ref: 662 Section Heading: Continuous Probability Distributions Keywords: continuous random variables AACSB: Application of knowledge

24) Integrating a function from zero to any value of a random variable x is an important step in determining the cumulative probability of that value of x. Answer: TRUE Diff: 2 Page Ref: 662 Section Heading: Continuous Probability Distributions Keywords: continuous random variables AACSB: Application of knowledge

25) ________ is a technique for selecting numbers randomly from a probability distribution. Answer: The Monte Carlo process Diff: 2 Page Ref: 648 Section Heading: Monte Carlo Simulation Keywords: random numbers AACSB: Application of knowledge

26) Developing the ________ probability distribution helps to determine random number ranges. Answer: cumulative Diff: 2 Page Ref: 659 Section Heading: Simulation of a Queuing System Keywords: computer mathematical simulation AACSB: Application of knowledge

4 .

27) Random numbers of a mathematical process instead of a physical process are ________ numbers. Answer: pseudorandom Diff: 2 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: random numbers, pseudo random numbers AACSB: Application of knowledge

28) Simulation models must be ________ to make sure they are accurately replicating the system being simulated. Answer: validated or verified Diff: 3 Page Ref: 676 Section Heading: Verification of the Simulation Model Keywords: simulation models AACSB: Application of knowledge

29) A table of random numbers must be ________ distributed, efficiently generated, and absent of patterns. Answer: uniformly Diff: 1 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: random numbers AACSB: Application of knowledge

30) The ________ command is used in generating the random numbers with Excel. Answer: RAND( ) Diff: 2 Page Ref: 654 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: simulation with Excel AACSB: Application of knowledge

31) In order to determine the value of discrete demand in a simulation model using Excel, the ________ function is used to associate a specific value of demand with a random number. Answer: VLOOKUP Diff: 2 Page Ref: 655 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: simulation with Excel AACSB: Application of knowledge

32) ________ is a risk analysis and forecasting program that uses Monte Carlo simulation. Answer: Crystal Ball Diff: 2 Page Ref: 669 Section Heading: Crystal Ball Keywords: computer simulation AACSB: Application of knowledge

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33) ________, ________, and ________ are common applications of simulation. Answer: There are many correct answers, including: queuing, inventory control, production/manufacturing, finance, marketing, public service operations, environmental and resource analysis. Diff: 2 Page Ref: 677 Section Heading: Areas of Simulation Application Keywords: simulation AACSB: Application of knowledge

34) In the Monte Carlo process, values for a random variable are generated by sampling from a(n) ________. Answer: probability distribution Diff: 2 Page Ref: 649 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

35) A long period of real time is represented by a short period of ________. Answer: simulated time Diff: 2 Page Ref: 649 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

36) The Monte Carlo process is analogous to and derives its name from ________. Answer: gambling devices Diff: 2 Page Ref: 649 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

37) ________ are numbers equally likely to be chosen from a large population of numbers. Answer: Random numbers Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Application of knowledge

38) A random number table features numbers that are derived from a(n) ________ process. Answer: artificial Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Application of knowledge

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39) Consider the following distribution and random numbers:

If a simulation begins with the first random number, what would the first simulation value would be ________. Answer: 2 Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Analytical thinking

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

40) Determine the drying time for these 5 random numbers: 0.13, 0.09, 0.19, 0.81, and 0.12. Answer:

Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Analytical thinking

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41) Determine the drying time for these 5 random numbers: 0.53, 0.95, 0.97, 0.96, and 0.07. Answer:

Diff: 2 Page Ref: 640 Section Heading: The Monte Carlo Process Keywords: simulation of a queuing system AACSB: Analytical thinking

42) The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

What is the average drying time if you simulate 10 trials using these random numbers: 0.13, 0.09, 0.19, 0.81, 0.12, 0.53, 0.95, 0.97, 0.96, and 0.07. Answer: 14.3 Diff: 3 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: simulation of a queuing system AACSB: Analytical thinking

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43) Determine the random number ranges for the data set (start with 00). Demand 5 6 7 8 9 Answer: Demand 5 6 7 8 9

Frequency 0.15 0.3 0.25 0.15 0.15 Random Number Ranges 00-14 15-44 45-69 70-84 85-99

Diff: 3 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random number ranges AACSB: Analytical thinking

44) Given the following random number ranges and the following random number sequence: 62, 13, 25, 40, 86, 93, determine the average demand for the following distribution of demand.

Demand 5 6 7 8 9

Random Number Ranges 00-14 15-44 45-69 70-84 85-99

Answer: 42/6 = 7 Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers, random number ranges AACSB: Analytical thinking

45) If f(x) = 2x, what is the equation for generating x, given the random number r? Answer: x = Diff: 2 Page Ref: 662 Section Heading: Continuous Probability Distributions Keywords: random numbers AACSB: Analytical thinking

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46) The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

Compute the mean drying time. Answer: 4.38 Diff: 3 Page Ref: 652 Section Heading: The Monte Carlo Process Keywords: mean, expected value AACSB: Analytical thinking

47) A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate two values from this distribution and has drawn these random numbers: -0.6 and 1.4. What are the two values, respectively? Answer: 470 and 570 Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: normal distribution AACSB: Analytical thinking

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48) The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following:

Determine the probability distribution of car arrivals. Answer: Number of Probability of Cars Arriving Occurrence 4 .05 5 .15 6 .35 7 .25 8 .20 Diff: 2 Page Ref: 640 Section Heading: The Monte Carlo Process Keywords: probability distribution AACSB: Analytical thinking

11 .

49) The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following:

Based on the above frequencies, use two-digit random numbers, start with random number 00, and determine the random number ranges for the data set given above. Answer: Number of Random Number Cars Arriving of Ranges 4 00-04 5 05-19 6 20-54 7 55-79 8 80-99 Diff: 2 Page Ref: 649 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Analytical thinking

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50) Consider the following manual simulation of machine breakdowns and repair.

Breakdowns 1 2 3 4 5 6 7 8 9 10

Time between breakdowns, x (weeks) 4 5.7 5.5 2.5 5.2 5.8 1.6 2.3 1.2 3.3

Repair time, y (days) 1 2 2 1 2 2 1 2 2 2

Cost ($2,000 y) $2000 $4000 $4000 $2000 $4000 $4000 $2000 $4000 $4000 $4000

What operating characteristics can be obtained from this simulation? Answer: Average time between breakdowns, average repair time, average cost. Depending on the length of the simulation run (quarterly, annual), total breakdowns and costs per time period could also be determined. Diff: 2 Page Ref: 660 Section Heading: Simulation of a Queuing System Keywords: simulation of a queuing system AACSB: Analytical thinking

51) George Pourbabaee owns a gas station. The cars arrive at the gas station according to the following inter-arrival time distribution. The time to service a car is given by the following service time distribution. Interarrival time (in minutes) 4 7 10 20

P(X)

Random Numbers

Service Time (in minutes)

P (X)

Random Numbers

.35 .25 .30 .10

00-34 35-59 60-89 90-99

2 4 6 8

.30 .40 .20 .10

00-29 30-69 70-89 90-99

Using the following random number sequence: 92, 44, 15, 97, 21, 80, 38, 64, 74, 08, estimate the average customer waiting time, average idle time of the assistant, and the average time a car spends in the system. Answer: Average idle time: 23/5 = 4.6 minutes Average waiting time = 7/5 = 1.4 minutes Average time in the system = 6.2 minutes Diff: 3 Page Ref: 660 Section Heading: Simulation of a Queuing System Keywords: Monte Carlo simulation AACSB: Analytical thinking

13 .

52) An answering service for a doctor's office wants to evaluate the service by simulation calls. They used past data to determine the distributions for the time between calls and the time spent on the phone with patients. Use the table below to manually simulate 8 calls. The time of the call and the service time have already been determined. Customer Number 1 2 3 4 5 6 7 8

Time of Call 15 45 70 95 125 150 175 205

Time call answered 15 45

190

Service Time 25 25 15 45 15 35 25 25

Time call Customer Operator ends Wait Time Wait Time 40 0 15 70 0 5

155

240

15 10

0 0

Calculate the average waiting time per customer. Calculate the utilization of the operator. Answer: Arrival Time of Time call Service Time call Customer Operator Number Call answered Time end Wait Time Wait Time 1 15 15 25 40 0 15 2 45 45 25 70 0 5 3 70 70 15 85 0 0 4 95 95 45 140 0 10 5 125 140 15 155 15 0 6 150 155 35 190 5 0 7 175 190 25 215 15 0 8 205 215 25 240 10 0 Average waiting time per customer = 5.625 minutes Utilization of operator = 87.5% Diff: 3 Page Ref: 660 Section Heading: Simulation of a Queuing System Keywords: manual simulation, operating characteristics AACSB: Analytical thinking

14 .

A graduate research assistant "moonlights" at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he's cooking an order, they have to wait until he's completed the current order. He is working on the simulation and a portion is shown below. 53) Complete the table below and determine the average customer wait time.

Customer Number

Time of Arrival

1 2 3 4 5

2 14 19 28 33

Time Order Taken 2 14

Customer Order Prep Customer Receives Time Wait Time Food 4 6 0 7 6 8 4

Time Order Taken 2 14 21 28 36

Customer Order Prep Customer Receives Time Wait Time Food 4 6 0 7 21 0 6 27 2 8 36 0 4 40 3

Answer: Customer Number

Time of Arrival

1 2 3 4 5

2 14 19 28 33

Average wait time = 1 minute Diff: 2 Page Ref: 660 Section Heading: Simulation of a Queuing System Keywords: manual simulation, operating characteristics AACSB: Analytical thinking

15 .

54) Complete the table and determine the average customer waiting time and the utilization of the cook.

Customer Number

Time of Arrival

1 2 3 4 5

2 14 19 28 33

Time Order Taken 2 14

Customer Order Prep Customer Cook "Idle" Receives Time Wait Time Time Food 4 6 0 2 7 6 8 4

Complete the table and determine the average customer waiting time and the utilization of the cook. Answer: Time Customer Customer Time of Order Prep Customer Cook "Idle" Order Receives Number Arrival Time Wait Time Time Taken Food 1 2 2 4 6 0 2 2 14 14 7 21 0 8 3 19 21 6 27 2 0 4 28 28 8 36 0 1 5 33 36 4 40 3 0 Average customer waiting time = 1 minute, utilization = 72.5% Diff: 2 Page Ref: 660 Section Heading: Simulation of a Queuing System Keywords: manual simulation AACSB: Analytical thinking

16 .

55) Assume that order prep time is based on the following distribution: Prep Time 3 4 5 6 7 8

Probability .10 .20 .25 .20 .15 .10

Complete the following table given that the random numbers for order prep time for customers 3, 4, and 5 are 62, 93, and 26, respectively.

Arrival Number

Time of Arrival

1 2 3 4 5

1 5 7 10 18

Time Order Taken 1 5

Customer Order Prep Customer Cook "Idle" Receives Time Wait Time Time Food 4 5 0 1 7 12 0 0

What is the average customer waiting time and the graduate student's utilization? Answer: Time Customer Arrival Time of Order Prep Customer Cook "Idle" Order Receives Number Arrival Time Wait Time Time Taken Food 1 1 1 4 5 0 1 2 5 5 7 12 0 0 3 7 12 6 18 5 0 4 10 18 8 26 8 0 5 18 26 4 30 8 0 Average wait time = 4.2 minutes; utilization = 96.67% Diff: 3 Page Ref: 660 Section Heading: Simulation of a Queuing System Keywords: manual simulation, utilization AACSB: Analytical thinking

17 .

A business professor wishes to model the duration of his commute through the busy streets of Bangalore. He decides to model it based on the number of auto-rickshaws that he passes during the first ten minutes of the drive. The continuous probability distribution 7x - 2 serves as a good model. 56) What is the integral from 0 to 4 for this distribution? Answer: The integral is 3.5x2 - 2x. When evaluated at 4 and 0, the values are 48 and 0, resulting in 48 - 0 = 48. Diff: 3 Page Ref: 662 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

After plowing through contracts for a decade, the contract writer knew about how long it took to crank out the material necessary to satisfy a contract's requirements. The distribution could be modeled using the data provided in this table. Number of Weeks 2 3 4 5 6

Random Number Range 0-5 6-15 16-35 36-80 81-99

57) If the first four random numbers are 17, 33, 64, and 8, what is the average number of weeks? Answer: The lookups are 4, 4, 5, and 3, for an average of 16/4 = 4 weeks. Diff: 1 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

58) If each contract is worth $4000 but it costs $200 per week to work on a contract, what is the profit resulting from a simulation drawing of the numbers 72, 36, 8, 71, and 94? Answer: $15,200 is the profit; revenues are $20,000 and expenses are 24 weeks @ $200/week Diff: 2 Page Ref: 651 Section Heading: Monte Carlo Simulation Keywords: Monte Carlo simulation AACSB: Analytical thinking

59) If the ten numbers generated are 87, 84, 99, 18, 81, 75, 32, 87, 46, and 35, what is the resultant expected average completion time? Answer: The average completion time is 5.2 weeks. Diff: 2 Page Ref: 651 Section Heading: Monte Carlo Simulation Keywords: Monte Carlo simulation AACSB: Analytical thinking

18 .

60) If each contract is worth $5000 but it costs $300 per week to work on a contract, what is the profit resulting from a simulation drawing of the numbers 72, 36, 8, 71, and 94 to represent contract durations? Answer: The total expenses are $7200 and the total revenue is 5 × $5000, for a profit of $17,800. Diff: 2 Page Ref: 651 Section Heading: Monte Carlo Simulation Keywords: Monte Carlo simulation AACSB: Analytical thinking

19 .

A newsboy sells newspapers and his goal is to maximize profit. He kept a record of his sales for 125 days with the following result: Newspapers demand per day 15 16 17 18 19 20 Total

Number of days 10 20 42 31 12 10 125

His ordering policy is to order an amount each day that is equal to the previous day's demand. A newspaper costs the carrier 50 cents and he sells it for $1.00. Unsold papers are returned and he receives 25 cents (for a loss of 25 cents). 61) Develop the cumulative distribution table and the corresponding random numbers. Newspapers demanded per day 15 16 17 18 19 20 Total

Number of Days

Probability

Cumulative Probability

10 20 42 31 12 10

Answer: Newspapers demanded Number of per day days 15 10 16 20 17 42 18 31 19 12 20 10 Total 125

Pr 0.08 0.16 0.336 0.248 0.096 0.08

Cum Pr. 0.08 0.24 0.58 0.82 0.92 1.00

Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

20 .

62) Use the information and random numbers given in the table below to simulate the sale of newspapers for 10 days.

Day

Demand

1 2 3 4 5 6 7 8 9 10

Random Number .78 .43 .93 .87 .48 .84 .87 .27 .20 .52

Quantity Ordered 18

Sales

Unsatisfied Demand

Unsold Papers

After completing the simulation, determine his total revenue for the ten days as well as monetary losses that result from unmet demand and unsold papers. Answer: Day 1 2 3 4 5 6 7 8 9 10

Demand 18 17 20 19 17 19 19 17 16 17

Random Number 0.78 0.43 0.93 0.87 0.48 0.84 0.87 0.27 0.2 0.52

Quantity Ordered 18 18 17 20 19 17 19 19 17 16 Total Revenue Cost of unsold papers Cost of unmet demand

Sales 18 17 20 19 17 19 19 17 16 17 179 $179.00

Unsatisfied Demand 0 0 3 0 0 2 0 0 0 1 6

$1.75

$3.00

Diff: 3 Page Ref: 652 Section Heading: Monte Carlo Simulation Keywords: Monte Carlo simulation AACSB: Analytical thinking

21 .

Unsold papers 0 1 0 1 2 0 0 2 1 0 7

Donuts Please The number of donuts needed for department meetings at the start of the semester can be modeled by the continuous probability distribution

, which we can integrate from 0 to some value x, which is the

number of days before the actual beginning of the semester. 63) What is the equation for generating x given the random number r? Answer:

-2

Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

64) What is the value for x when random number r is equal to six? Answer: 18, a dozen and a half of delicious donuts. Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

65) Analogue simulation replaces a physical system with an analogous physical system that is ________ to manipulate. A) harder B) easier C) equally difficult D) more expensive Answer: B Diff: 2 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: Analogue simulation, Monte Carlo simulation AACSB: Application of knowledge

66) ________ is a technique for selecting numbers randomly from a probability distribution. A) Marseille B) Monaco C) Monte Carlo D) Analogue simulation Answer: C Diff: 1 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

22 .

67) In the Monte Carlo process, values for a random variable are generated by ________ a probability distribution. A) sampling from B) running C) integrating D) implementing Answer: A Diff: 2 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

68) The ________ process is analogous to gambling devices. A) Simulation B) Monte Carlo C) Monaco D) none of the above Answer: B Diff: 2 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

69) ________ numbers are numbers derived from a mathematical process that appear to be random. A) Random B) Pseudorandom C) Randomized D) Semi-random Answer: B Diff: 1 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: pseudorandom numbers AACSB: Application of knowledge

70) Pseudorandom numbers exhibit a ________ in order to be considered truly random. A) limited number of possible outcomes B) uniform distribution C) detectable pattern D) detectable run of certain numbers Answer: B Diff: 3 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: pseudorandom numbers AACSB: Application of knowledge

23 .

71) ________ is not part of a Monte Carlo simulation. A) Analyzing results B) Analyzing a real problem C) Finding an optimal solution D) Evaluating the results Answer: C Diff: 1 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

72) A seed value is a(n): A) steady state solution of a simulation experiment. B) number used to start a stream of random numbers. C) first run of a simulation model. D) analytic solution of a simulation experiment. Answer: B Diff: 2 Page Ref: 673 Section Heading: Crystal Ball Keywords: random numbers AACSB: Application of knowledge

73) In assigning random numbers to probabilistic events in a simulation: A) several events are associated with the same random number. B) every random number is associated with a particular event. C) every event is associated with the same random number. D) the events dictate the seed number of the random number stream. Answer: B Diff: 2 Page Ref: 649 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Application of knowledge

74) ________ are the values that express the state of the system being modeled at the beginning of the Monte Carlo simulation. A) Outputs B) Random events C) Initial conditions D) Random numbers Answer: C Diff: 2 Page Ref: 652 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Application of knowledge

24 .

75) Simulation does not usually provide recommended decisions. Instead it provides: A) operating characteristics. B) optimal solutions. C) realistic results. D) system parameters. Answer: A Diff: 1 Page Ref: 648 Section Heading: The Monte Carlo Process Keywords: simulation models, optimal solutions AACSB: Application of knowledge

76) For the following frequency distribution of demand, the random number 0.23 would be interpreted as a demand of:

A) 0 B) 1 C) 2 D) 3 Answer: A Diff: 1 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Analytical thinking

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Consider the following frequency of demand and random numbers:

Random numbers: 0.13, 0.81, 0.53. 77) If the simulation begins with the first random number, the simulated value for demand would be: A) 0 B) 1 C) 2 D) 3 Answer: A Diff: 1 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Analytical thinking

78) If the simulation begins with the second random number, the simulated value for demand would be: A) 1 B) 2 C) 3 D) 4 Answer: C Diff: 1 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Analytical thinking

79) If the simulation begins with the third random number, the simulated value for demand would be: A) 0 B) 1 C) 2 D) 3 E) 4 Answer: C Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: random numbers AACSB: Analytical thinking

26 .

Random Number Range 0-5 6-15 16-35 36-80 81-99

80) Using the random number table 14.3 in your text, column 1, reading across row 1, what is the average length of the next five contracts? A) 5 B) 6 C) 4 D) 3 Answer: A Diff: 1 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

81) Using the random number table 14.3 in your text, column 1, reading across row 1, what is the standard deviation of the average length of the next five contracts? A) 1 B) 0 C) 1.414 D) 5 Answer: B Diff: 2 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

82) Using the random number table 14.3 in your text, column 1, reading across row 2, what is the average length of the next five contracts? A) 4.6 B) 4.8 C) 5.0 D) 5.2 Answer: C Diff: 2 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

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83) Using the random number table 14.3 in your text, column 1, reading across row 2, what is the standard deviation of the average length of the next five contracts? A) 0.50 B) 0.55 C) 0.60 D) 0.63 Answer: D Diff: 2 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

84) Using the random number table 14.3 in your text, column 1, reading across row 3, what is the average length of the next five contracts? A) 4.6 B) 4.8 C) 5.0 D) 5.2 Answer: B Diff: 2 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

85) Using the random number table 14.3 in your text, column 1, reading across row 3, what is the standard deviation of the average length of the next five contracts? A) 0.75 B) 0.70 C) 0.65 D) 0.60 Answer: A Diff: 2 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

86) Using the random number table 14.3 in your text, column 1, reading across row 6, what is the average length of the next five contracts? A) 4.6 B) 4.4 C) 4.2 D) 4.0 Answer: D Diff: 2 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

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87) Using the random number table 14.3 in your text, column 1, reading across row 6, what is the standard deviation of the average length of the next five contracts? A) 1.414 B) 1.250 C) 1.166 D) 1.083 Answer: A Diff: 2 Page Ref: 651 Section Heading: The Monte Carlo Process Keywords: Monte Carlo simulation AACSB: Analytical thinking

88) Which of the following would not be considered a limitation of simulation modeling? A) Models are typically unstructured. B) Validation of simulation models can be difficult. C) The cost of building simulation can be prohibitive. D) Simulation allows flexibility in analyzing systems. Answer: D Diff: 1 Page Ref: 678 Section Heading: Verification of the Simulation Model Keywords: simulation models, limitations AACSB: Application of knowledge

89) Simulations are normally done: A) manually. B) in a casino. C) by a spreadsheet. D) on the computer. Answer: D Diff: 1 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: computer simulation AACSB: Application of knowledge

90) Random numbers generated by a ________ process instead of a ________ process are pseudorandom numbers. A) physical, physical B) physical, mathematical C) mathematical, physical D) mathematical, mathematical Answer: C Diff: 2 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: random numbers AACSB: Application of knowledge

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91) A table of random numbers must be: A) in descending order. B) efficiently generated. C) normally distributed. D) in ascending order. Answer: B Diff: 2 Page Ref: 653 Section Heading: Computer Simulation with Excel Spreadsheets Keywords: random numbers AACSB: Application of knowledge

92) Developing the cumulative probability distribution helps to determine: A) simulation numbers. B) data sets. C) random number ranges. D) mean of the distribution. Answer: C Diff: 2 Page Ref: 659 Section Heading: Simulation of a Queuing System Keywords: cumulative probability distribution AACSB: Application of knowledge

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Customer Number

Time of Arrival

1 2 3 4 5

2 14 19 28 33

Time Order Taken 2 14

Customer Order Prep Customer Receives Time Wait Time Food 4 6 0 7 6 8 4

93) Average customer waiting time is: A) 1 minute. B) 2 minutes. C) 2.5 minutes. D) 3 minutes. Answer: A Diff: 3 Page Ref: 658 Section Heading: Simulation of a Queuing System Keywords: manual simulation, waiting time AACSB: Analytical thinking

94) Average utilization is: A) 67%. B) 72.5%. C) 83.4%. D) 95%. Answer: B Diff: 3 Page Ref: 658 Section Heading: Simulation of a Queuing System Keywords: manual simulation, waiting time AACSB: Analytical thinking

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95) ________ simulation is limited because of the amount of real time required to simulate even one trial. A) Manual B) Monte Carlo C) Monaco D) Any kind of Answer: A Diff: 3 Page Ref: 653 Section Heading: Continuous Probability Distributions Keywords: manual simulation AACSB: Application of knowledge

A business professor wishes to model the duration of his commute through the busy streets of Bangalore. He decides to model it based on the number of auto-rickshaws that he passes during the first ten minutes of the drive. The continuous probability distribution 7x - 2 serves as a good model. 96) What is the integral from 0 to 4 for this distribution? A) 48 B) 38 C) 26 D) 20 Answer: A Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

97) What is the integral from 0 to 5 for this distribution? A) 33 B) 77.5 C) 59 D) 63 Answer: B Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

98) What is the integral from 5 to 7 for this distribution? A) 14 B) 36 C) 80 D) 66 Answer: C Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

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99) What is the integral from 8 to 9 for this distribution? A) 7 B) 23.5 C) 40 D) 57.5 Answer: D Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

Donuts Please The number of donuts needed for department meetings at the start of the semester can be modeled by the continuous probability distribution

, which we can integrate from 0 to some value x, which is the

number of days before the actual beginning of the semester. 100) What is the equation for generating x given the random number r? A)

-2

B) er - 2 C) ln( ) - 2 D) ln(r) - 2 Answer: A Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

101) What is the value for x when random number r is equal to two? A) 0.117 B) 0.718 C) 2.482 D) 5.389 Answer: B Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

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102) What is the value for x when random number r is equal to ten? A) 18.09 B) 52.59 C) 146.41 D) 401.43 Answer: C Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

103) What is the value for x when random number r is equal to six? A) 2 B) 5 C) 10 D) 18 Answer: D Diff: 3 Page Ref: 663 Section Heading: Continuous Probability Distributions Keywords: continuous probability distributions, continuous random variables AACSB: Analytical thinking

104) If the probability of an event is 0.36, what random number range specifies this properly? A) 0.10 - 0.20 B) 0.20 - 0.30 C) 0.30 - 0.40 D) 0.40 - 0.50 Answer: C Diff: 1 Page Ref: 658 Section Heading: Simulation of a Queuing System Keywords: random numbers AACSB: Analytical thinking

105) Sometimes manual simulation of several trials is ________ way to validate a simulation. A) a good B) a bad C) no D) the only Answer: A Diff: 2 Page Ref: 676 Section Heading: Verification of the Simulation Model Keywords: manual simulation AACSB: Application of knowledge

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106) Unlike optimization models, simulation provides: A) recommendations. B) operating characteristics. C) suggestions. D) solutions . Answer: B Diff: 2 Page Ref: 678 Section Heading: Areas of Simulation Application Keywords: operating characteristics AACSB: Application of knowledge

107) A limitation of simulation is that: A) models are typically well-structured and must be developed for problems that are also wellstructured. B) it is usually possible to realistically validate simulation results. C) model building is costly and time-consuming. D) it is more difficult to manipulate the elements of a computer simulation than the actual system. Answer: C Diff: 2 Page Ref: 678 Section Heading: Areas of Simulation Application Keywords: simulation models AACSB: Application of knowledge

The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows: Yield, bushels per acre 350 400 450 500

Probability .10 .18 .50 .22

The estimated average price per bushel is $16.80. 108) What is the expected yield of the crop? A) 425 B) 442 C) 440 D) 475 Answer: B Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: expected value AACSB: Analytical thinking

35 .

109) Use the following random numbers to simulation crop yield for 10 years: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81. What is the estimated crop yield from the simulation? A) 425 B) 442 C) 440 D) 475 Answer: C Diff: 2 Page Ref: 650 Section Heading: The Monte Carlo Process Keywords: simulation results AACSB: Analytical thinking

A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 10-minute intervals, the following probability distribution and random number assignments developed. Number of Arrivals 6 7 8 9 10

Probability .1 .3 .3 .2 .1

Random numbers .01 - .10 .11 - .40 .41 - .70 .71 - .90 .91 - .00

110) Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period? A) 22 B) 23 C) 24 D) 25 Answer: C Diff: 2 Page Ref: 658 Section Heading: Simulation of a Queuing System Keywords: manual simulation, waiting time AACSB: Analytical thinking

111) Suppose the next three random numbers were .08, .50 and .69. How many customers would have arrived during this 30-minute period? A) 22 B) 23 C) 24 D) 25 Answer: A Diff: 2 Page Ref: 658 Section Heading: Simulation of a Queuing System Keywords: manual simulation, waiting time AACSB: Analytical thinking

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112) Suppose the next three random numbers were .11, .42 and .84. Use these values to simulate arrivals into the bakery and determine the average number of arrivals per 10-minute period based on these occurrences. The average number of arrivals per 10-minute period is: A) 6. B) 7. C) 8. D) 9. Answer: C Diff: 3 Page Ref: 658 Section Heading: Simulation of a Queuing System Keywords: manual simulation, waiting time AACSB: Analytical thinking

Two hundred simulation runs were completed using the probability of a machine breakdown from the table below. The average number of breakdowns from the simulation trials was 1.93 with a standard deviation of 0.20. No. of breakdowns per week 0 1 2 3 4

Probability

Cumulative probability

.10 .25 .36 .22 .07

.10 .35 .71 .93 1.00

113) What is the probability of 2 or fewer breakdowns? A) .25 B) .35 C) .36 D) .71 Answer: D Diff: 1 Page Ref: 659 Section Heading: Simulation of a Queuing System Keywords: simulation results AACSB: Analytical thinking

114) What is the probability that there are more than 3 breakdowns? A) .07 B) .10 C) .22 D) .25 Answer: A Diff: 1 Page Ref: 659 Section Heading: Simulation of a Queuing System Keywords: simulation results AACSB: Analytical thinking

37 .

115) Construct a 95% confidence interval for the average number of machine breakdowns. A) 1.896 to 1.938 B) 1.902 to 1.958 C) .1.877 to 1.943 D) 1.907 to 1.953 Answer: B Diff: 3 Page Ref: 667 Section Heading: Statistical Analysis of Simulation Results Keywords: simulation results AACSB: Analytical thinking

116) A 95% confidence interval is (54.5, 57.5) based on a sample size of 25. What is the sample standard deviation? A) 3.826 B) 19.132 C) 8.973 D) 11.646 Answer: A Diff: 3 Page Ref: 667 Section Heading: Statistical Analysis of Simulation Results Keywords: confidence interval AACSB: Analytical thinking

117) What is the 95% confidence interval width for a sample with a mean of 50 and a standard deviation of 14 based on 75 observations? A) (44.13, 55.87) B) (46.83, 53.17) C) (40.67, 59.32) D) (48.22, 51.78) Answer: B Diff: 3 Page Ref: 667 Section Heading: Statistical Analysis of Simulation Results Keywords: confidence interval AACSB: Analytical thinking

118) The use of simulation to determine the impact of projects such as nuclear power plants, reservoirs and dams is known as: A) public service operation. B) environmental and resource analysis. C) cost benefit analysis. D) project management. Answer: B Diff: 1 Page Ref: 677 Section Heading: Areas of Simulation Application Keywords: simulation applications AACSB: Application of knowledge

38 .

119) The use of simulation to analyze airport operations, and fire or police department operations are known as: A) public service operation. B) environmental and resource analysis. C) cost benefit analysis. D) operations management. Answer: A Diff: 1 Page Ref: 677 Section Heading: Areas of Simulation Application Keywords: simulation applications AACSB: Application of knowledge

39 .

Introduction to Management Science, 12e (Taylor) Chapter 15 Forecasting 1) A trend is a gradual, long-term, up-or-down movement of demand. Answer: TRUE Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: trend, forecasting components AACSB: Application of knowledge

2) A seasonal pattern is an up-and-down repetitive movement within a trend occurring periodically. Answer: TRUE Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: seasonal pattern, forecasting components AACSB: Application of knowledge

3) Random variations are movements that are not predictable and follow no pattern. Answer: TRUE Diff: 2 Page Ref: 700 Section Heading: Forecasting Components Keywords: random variations, forecasting components AACSB: Application of knowledge

4) The basic types of forecasting methods include time series, regression, and qualitative methods. Answer: TRUE Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: types of forecasting methods AACSB: Application of knowledge

5) Time series is a category of statistical techniques that uses historical data to predict future behavior. Answer: TRUE Diff: 1 Page Ref: 701 Section Heading: Forecasting Components Keywords: time series analysis AACSB: Application of knowledge

6) Regression methods attempt to develop a mathematical relationship between the item being forecast and factors that cause it to behave the way it does. Answer: TRUE Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: regression methods AACSB: Application of knowledge

1 .

7) Qualitative methods use management judgment, expertise, and opinion to make forecasts. Answer: TRUE Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: qualitative methods AACSB: Application of knowledge

8) Qualitative methods are the least common type of forecasting method for the long-term strategic planning process. Answer: FALSE Diff: 1 Page Ref: 701 Section Heading: Forecasting Components Keywords: qualitative methods AACSB: Application of knowledge

9) A cycle is an up-or-down movement in demand that repeats itself in less than 1 year. Answer: FALSE Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: regression methods AACSB: Application of knowledge

10) Seasonal patterns are observed only during the four seasons - winter, spring, summer, and fall. Answer: FALSE Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: time series methods AACSB: Application of knowledge

11) The Delphi method develops a consensus forecast about what will occur in the future. Answer: TRUE Diff: 2 Page Ref: 703 Section Heading: Forecasting Components Keywords: Delphi method, qualitative methods AACSB: Application of knowledge

12) Technological forecasting helps determine the technological feasibility of new products by surveying large numbers of consumers. Answer: FALSE Diff: 1 Page Ref: 703 Section Heading: Forecasting Components Keywords: technological forecasting AACSB: Application of knowledge

13) Irregular variations exhibit no pattern. Answer: TRUE Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: forecasting components, irregular variation AACSB: Application of knowledge

2 .

14) Data cannot exhibit both trend and cyclical patterns. Answer: FALSE Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: forecasting components, trend, cyclical AACSB: Application of knowledge

15) Time series methods assume that what has occurred in the past will continue to occur in the future. Answer: TRUE Diff: 1 Page Ref: 703 Section Heading: Time Series Methods Keywords: time series methods AACSB: Application of knowledge

16) Moving averages are good for stable demand with no pronounced behavioral patterns. Answer: TRUE Diff: 2 Page Ref: 703 Section Heading: Time Series Methods Keywords: moving averages AACSB: Application of knowledge

17) Longer-period moving averages react more slowly to recent demand changes than do shorter-period moving averages. Answer: TRUE Diff: 2 Page Ref: 705 Section Heading: Time Series Methods Keywords: moving averages AACSB: Analytical thinking

18) Shorter-period moving averages react more slowly to recent demand changes than do longer-period moving averages. Answer: FALSE Diff: 2 Page Ref: 705 Section Heading: Time Series Methods Keywords: moving averages AACSB: Analytical thinking

19) In a weighted moving average, weights must sum to 1. Answer: TRUE Diff: 1 Page Ref: 706 Section Heading: Time Series Methods Keywords: moving averages, weighted moving average, time series methods AACSB: Application of knowledge

20) Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality. Answer: FALSE Diff: 1 Page Ref: 710 Section Heading: Time Series Methods Keywords: adjusted exponential smoothing AACSB: Application of knowledge

3 .

21) If average forecast error is positive, it indicates that the forecast is biased high. Answer: FALSE Diff: 2 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: forecast error AACSB: Analytical thinking

22) Regression is used to relate one variable to one or more variables. Answer: TRUE Diff: 1 Page Ref: 723 Section Heading: Regression Methods Keywords: regression methods, linear regression AACSB: Application of knowledge

23) The dependent variable in linear regression is usually designated as the x variable. Answer: FALSE Diff: 2 Page Ref: 723 Section Heading: Regression Methods Keywords: regression methods, linear regression AACSB: Application of knowledge

24) In the regression equation y=a+bx, the slope of the equation is x. Answer: FALSE Diff: 2 Page Ref: 723 Section Heading: Regression Methods Keywords: regression methods, linear regression AACSB: Application of knowledge

25) Correlation measures the strength of relationship between the x and y variables and the closer it is to 1 or -1, the greater the proof that the level of x determines the level of y. Answer: FALSE Diff: 2 Page Ref: 725 Section Heading: Regression Methods Keywords: regression methods, linear regression AACSB: Application of knowledge

26) The coefficient of determination provides a measure of how the level of the independent variable in a regression equation explains the level of the dependent variable in the equation. Answer: TRUE Diff: 2 Page Ref: 723 Section Heading: Regression Methods Keywords: regression methods, linear regression AACSB: Application of knowledge

27) ________ is a gradual, long-term, upward or downward movement of demand. Answer: Trend Diff: 2 Page Ref: 700 Section Heading: Forecasting Components Keywords: trend AACSB: Application of knowledge

4 .

28) A(n) ________ forecast typically encompass a period longer than one year. Answer: long-range Diff: 2 Page Ref: 700 Section Heading: Forecasting Components Keywords: long range forecasts AACSB: Application of knowledge

29) Daily operations are assisted by ________-range forecasting. Answer: short Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: short range forecasts AACSB: Application of knowledge

30) Unpredictable movements in demand that follow no pattern are ________. Answer: random variations Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: forecasting components, irregular variation AACSB: Application of knowledge

31) The major types of forecasting methods are ________, ________, and ________. Answer: time series, regression, qualitative Diff: 1 Page Ref: 701 Section Heading: Forecasting Components Keywords: forecasting methods AACSB: Application of knowledge

32) Knowledgeable individuals bring their opinions to bear in ________, a qualitative method of forecasting. Answer: the Delphi method Diff: 1 Page Ref: 703 Section Heading: Forecasting Components Keywords: Delphi method, qualitative methods AACSB: Application of knowledge

33) A long-term wave in a demand pattern that undulates gracefully over a period of greater than a year is a(n) ________. Answer: cycle Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: forecasting components, trend, cyclical AACSB: Application of knowledge

34) ________ error is the sum of the forecast errors. Answer: Cumulative Diff: 2 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: medium range forecasts AACSB: Application of knowledge

5 .

35) A(n) ________ forecast encompasses the immediate future, is concerned with daily activities of the firm and does not go beyond one or two months in to the future. Answer: short-range Diff: 2 Page Ref: 700 Section Heading: Forecasting Components Keywords: short range forecasts AACSB: Application of knowledge

36) A(n) ________ is an up-and-down repetitive movement within a trend occurring periodically. Answer: seasonal pattern Diff: 2 Page Ref: 700 Section Heading: Forecasting Components Keywords: seasonal pattern, forecasting components AACSB: Application of knowledge

37) ________ relates demand to two or more independent variables. Answer: Multiple regression Diff: 2 Page Ref: 729 Section Heading: Regression Methods Keywords: multiple linear regression analysis AACSB: Application of knowledge

38) One problem with multiple regression is ________, which is a measure of the amount of "overlapping" information about the dependent variable that's provided by several independent variables. Answer: multicollinearity Diff: 2 Page Ref: 732 Section Heading: Regression Methods Keywords: simple exponential smoothing AACSB: Application of knowledge

39) Exponential smoothing forecasts are more sensitive or reactive to the changes in demand as the value of the smoothing constant, α, ________. Answer: increases Diff: 2 Page Ref: 708 Section Heading: Time Series Keywords: simple exponential smoothing AACSB: Analytical thinking

40) The closer the value of α is to zero, the ________ will be the dampening or smoothing effect. Answer: greater Diff: 2 Page Ref: 708 Section Heading: Time Series Keywords: simple exponential smoothing AACSB: Analytical thinking

41) ________ measures the strength of the relationship between two variables. Answer: Correlation Diff: 2 Page Ref: 7726 Section Heading: Regression Methods Keywords: correlation, regression methods, linear regression model AACSB: Application of knowledge

6 .

42) The ________ is the percentage of variation in the dependent variable that results from the independent variable. Answer: coefficient of determination Diff: 2 Page Ref: 726 Section Heading: Regression Methods Keywords: coefficient of determination, reg methods, linear reg model AACSB: Analytical thinking

43) Longer-period moving averages react more ________ to recent demand changes than do shorter period moving averages. Answer: slowly Diff: 2 Page Ref: 704 Section Heading: Time Series Keywords: moving average method AACSB: Analytical thinking

44) ________ are the movements or fluctuation in demand that exhibit no pattern and occur on a random basis. Answer: Random variations Diff: 2 Page Ref: 700 Section Heading: Time Series Keywords: forecasting components, irregular variation AACSB: Application of knowledge

45) The ________ is the sum of the absolute value of forecasting errors divided by the number of periods in which a forecast was made. Answer: MAD or mean absolute deviation Diff: 1 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: forecast error, MAD AACSB: Application of knowledge

46) The ________ is the average of the sum of the squared errors. Answer: MSE or mean squared error Diff: 1 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: forecast error, MSE AACSB: Application of knowledge

47) MAPD measures ________. Answer: the absolute error as a percentage of the actual (demand) data Diff: 2 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: forecast error, MAPD AACSB: Application of knowledge

7 .

48) ________ is a type of exponential smoothing that can also include trend. Answer: Adjusted exponential smoothing Diff: 1 Page Ref: 710 Section Heading: Time Series Keywords: adjusted exponential smoothing AACSB: Application of knowledge

Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

49) Compute a 3-period moving average for period 4. Answer: 211.67 Diff: 2 Page Ref: 704 Section Heading: Time Series Keywords: moving averages, time series methods AACSB: Analytical thinking

50) Compute a 3-period moving average for period 6. Answer: 246.67 Diff: 2 Page Ref: 704 Section Heading: Time Series Keywords: moving averages, time series methods AACSB: Analytical thinking

51) Compute a 3-period moving average for period 7. Answer: 283.33 Diff: 2 Page Ref: 704 Section Heading: Time Series Keywords: moving averages, time series methods AACSB: Analytical thinking

52) Compute a 5-period moving average for period 6. Answer: 237 Diff: 3 Page Ref: 704 Section Heading: Time Series Keywords: moving averages, time series methods AACSB: Analytical thinking

8 .

53) Compute a 5-period moving average for period 7. Answer: 257 Diff: 3 Page Ref: 704 Section Heading: Time Series Keywords: moving averages, time series methods AACSB: Analytical thinking

54) Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 2-day moving average. Answer: 91 Diff: 1 Page Ref: 704 Section Heading: Time Series Keywords: moving average method AACSB: Analytical thinking

55) Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 3-day moving average. Answer: 92.3 Diff: 1 Page Ref: 704 Section Heading: Time Series Keywords: moving average method, forecast error AACSB: Analytical thinking

56) Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast for today using a weighted moving average, with a weights of .6, .3, and .1, where the highest weights are applied to the most recent data. Answer: 91.7 = .6(92) + .3(90) + .1(95) Diff: 2 Page Ref: 706 Section Heading: Time Series Keywords: weighted moving average AACSB: Analytical thinking

Given the following data on hotel check-ins for a 6-month period: July: August: September: October: November: December:

70 rooms 105 rooms 90 rooms 120 rooms 110 rooms 115 rooms

57) What is the 3-month moving average forecast for January? Answer: 115 Diff: 2 Page Ref: 704 Section Heading: Time Series Keywords: moving averages, time series methods AACSB: Analytical thinking

9 .

58) With alpha = 0.2, what is the simple exponential smoothing forecast for October? Assume the forecast for July was 80 rooms. Answer: Demand Forecast July 70 80 Aug 105 78 Sept 90 83.4 Oct 120 84.72 Nov 110 91.776 Dec 115 95.421 October forecast is 84.72 Diff: 2 Page Ref: 707 Section Heading: Time Series Keywords: simple exponential smoothing, exponential smoothing AACSB: Analytical thinking

59) Using a 3-month moving average, how many check-ins can be forecasted for January? Answer: 115 Diff: 1 Page Ref: 704 Section Heading: Time Series Keywords: moving averages AACSB: Analytical thinking

60) Using the exponential smoothing factor 0.3, how many check-ins can be forecasted for January? Assume the forecast for December was 122 rooms. Answer: 119.9 Diff: 3 Page Ref: 707 Section Heading: Time Series Keywords: exponential smoothing AACSB: Analytical thinking

61) The following data summarizes the historical demand for a product. Month March April May June July August

Actual Demand 20 25 40 35 30 45

Use exponential smoothing with α = .2 and a smoothed forecast for July of 32 to determine August and September's smoothed forecasts. Answer: FAugust = 31.6, FSeptember = 34.28 Diff: 2 Page Ref: 707 Section Heading: Time Series Keywords: simple exponential smoothing AACSB: Analytical thinking

10 .

62) If the forecast is 33 and the actual value is 44, then the error this period is ________. Answer: 11 Diff: 1 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: forecast accuracy AACSB: Analytical thinking

63) If the forecast is 25 and the actual value is 25, then the error this period is ________. Answer: 0 Diff: 1 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: forecast accuracy AACSB: Analytical thinking

64) The following sales data are available for 2003-2008:

Determine a 4-year moving average forecast for 2008 and 2009. Answer: F2008 = 15.5, F2009 = 18.75 Diff: 2 Page Ref: 704 Section Heading: Time Series Keywords: moving average method AACSB: Analytical thinking

65) The following sales data are available for 2003-2008: Year 2003 2004 2005 2006 2007 2008

Sales 7 12 14 20 16 25

Forecast 9 10 15 22 18 21

Calculate the average error. Answer: = -0.167 Diff: 2 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: moving average method AACSB: Analytical thinking

11 .

66) If the forecast is 14 and the actual value is 15, then the error this period is ________. Answer: 1 Diff: 1 Page Ref: 716 Section Heading: Time Series Keywords: forecast accuracy AACSB: Analytical thinking

67) If the absolute errors were calculated for 5 periods and the sum of the absolute deviation is 60, what is the value of the MAD? Answer: 12 Diff: 2 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: Mean Absolute Deviation AACSB: Analytical thinking

68) Assume that the forecasted demand for 2006 is 15. Use the following data set and exponential smoothing with α = 0.4 and determine the forecasted demand for 2009.

Answer: F2007 = 15.4, F2008 = 17.24, F2009 = 17.544 Diff: 2 Page Ref: 708 Section Heading: Time Series Keywords: simple exponential smoothing AACSB: Analytical thinking

69) Given the following data, compute the MAD for the forecast. Year 2001 2002 2003

Demand 16 20 18

Forecast 18 19 24

Answer: MAD = 3 Diff: 2 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: simple exponential smoothing, forecast error, forecast accuracy AACSB: Analytical thinking

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70) The following sales data are available for 2003-2008.

Determine a 4-year weighted moving average forecast for 2009, where weights are W 1 = .1, W2 = .2, W3 = .2 and W4 = .5. Answer: F2009 = 21.1 Diff: 2 Page Ref: 706 Section Heading: Time Series Keywords: weighted moving average AACSB: Analytical thinking

71) Quarterly sales is given for the past 3 years. Determine the seasonal factors for each quarter.

Year 1 Year 2 Year 3

Winter 4800 5700 6000

Spring 4500 3800 4600

Summer 4100 4500 4900

Fall 5500 6000 6500

Answer: Swinter = .27, Sspring = .2118, Ssummer = .2217, Sfall = .2956 Diff: 2 Page Ref: 714 Section Heading: Time Series Keywords: seasonal factors AACSB: Analytical thinking

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Recent past demand for product ZXT is given in the following table.

Month February March April May June July August

Actual Demand 20 22 33 35 31 48 41

72) Determine the forecasted demand for April and May based on adjusted exponential smoothing with α = .2, β = .3, a February forecast of 20, and T = 0. Answer: AFApril = 20.52, AFMay = 23.884 Diff: 3 Page Ref: 710 Section Heading: Time Series Keywords: adjusted exponential smoothing method AACSB: Analytical thinking

73) Base on a three-month weighted moving average with weights w1 = .1, w2 = .4, and w3 = .5 (most recent), determine the forecasted demand for August and September. What is the forecast error in August? Answer: FAugust = 39.9, FSeptember = 42.8, eAugust = 1.1 Diff: 2 Page Ref: 716 Section Heading: Time Series Keywords: moving avg method, weighted moving avg method, forecast error AACSB: Analytical thinking

74) Use simple exponential smoothing with alpha = .4 and determine the forecasted demand for August and September. Assume that the smoothed forecast for July is 38. Answer: FAugust = 42, FSeptember = 41.6 Diff: 2 Page Ref: 707 Section Heading: Time Series Keywords: simple exponential smoothing AACSB: Analytical thinking

75) Simple exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be four units less than actual demand. If the next forecast is 66.6, what is the value of the smoothing constant, α? Answer: 0.15 Diff: 2 Page Ref: 707 Section Heading: Time Series Keywords: exponential smoothing AACSB: Analytical thinking

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76) Robert wants to know if there is a relation between money spent on gambling and winnings.

What is the coefficient of determination? Answer: 0.94117 Diff: 3 Page Ref: 726 Section Heading: Regression Models Keywords: regression models, coefficient of determination AACSB: Analytical thinking

Robert has the following accounts on money spent on gambling and winnings:

77) Develop a regression equation that relates the money Robert spends and the money he wins. Answer: Y = 2613.3 + 0.8383 X, where Y = money won Diff: 3 Page Ref: 724 Section Heading: Regression Models Keywords: linear regression models, regression analysis AACSB: Analytical thinking

78) Determine the correlation coefficient and the coefficient of determination. Answer: r2 =.835 and r = .913 Diff: 3 Page Ref: 726 Section Heading: Regression Models Keywords: linear regression models, regression analysis AACSB: Analytical thinking

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Sally has been running the following number of ads in the local newspaper to help attract customers into her store. She has also been keeping track of customers who have come into the store as a result of the ads, as well as the amount of money they spend. This is the data from the last 4 weeks:

79) Determine the equation that relates ads and increased sales. Answer: Y = 50 + 18X Diff: 3 Page Ref: 725 Section Heading: Regression Models Keywords: regression analysis, linear regression models AACSB: Analytical thinking

80) If Sally runs 15 ads, how much will sales increase? Answer: Y = 50 + 18(15) = 320 Diff: 3 Page Ref: 725 Section Heading: Regression Models Keywords: regression analysis, linear regression models AACSB: Analytical thinking

81) If Sally runs 10 ads, how much will sales increase? Answer: Cannot say, because 10 it outside the range of values for the independent variable. However, a student using the regression equation may suggest that a sales increase of $230 is reasonable. Diff: 3 Page Ref: 716 Section Heading: Regression Models Keywords: regression analysis, linear regression models AACSB: Analytical thinking

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Consider the following annual sales data for 2001-2008: Year 2001 2002 2003 2004 2005 2006 2007 2008

Sales 2 4 10 8 14 18 17 20

82) Use the linear regression method and determine the estimated sales equation. Answer: Y = -.2143 + 2.6309 X. This equation is appropriate if years are treated as 1, 2, 3, etc. Y = -5262.12 + 2.6309 X. This equation is appropriate if years are treated as 2001, 2002, 2003, etc. Diff: 2 Page Ref: 726 Section Heading: Regression Models Keywords: regression analysis, linear regression method AACSB: Analytical thinking

83) Calculate the coefficient of determination. Answer: r2 = .93217 Diff: 2 Page Ref: 726 Section Heading: Regression Models Keywords: correlation coefficient and the coefficient of determination AACSB: Analytical thinking

84) Calculate the correlation coefficient. Answer: r = .96548 Diff: 2 Page Ref: 726 Section Heading: Regression Models Keywords: correlation coefficient and the coefficient of determination AACSB: Analytical thinking

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A rendering plant wishes to use the data (sales records from a few local businesses and the month of the year) to help determine their supply level for the coming months. The records shown in the table provide an excellent opportunity for you to assist them with their forecasting. Month January February March April May June

Sales 45 57 32 44 51 34

Pounds 54.3 63.8 39.5 49.8 52.3 39.9

85) What is the regression equation resulting from using Sales to forecast Pounds? Answer: Pounds = 9.52 + 0.922 × Sales Diff: 2 Page Ref: 723 Section Heading: Regression Methods Keywords: regression methods AACSB: Analytical thinking

86) What is the regression equation resulting from using the month, where January = 1, February = 2, etc.) to forecast Pounds? Answer: Pounds = 59.55 -2.74 × Month Diff: 2 Page Ref: 723 Section Heading: Regression Methods Keywords: regression methods AACSB: Analytical thinking

87) What is the regression equation resulting from using both the month (where January = 1, February = 2, etc.) and the level of Sales to forecast Pounds? Answer: Pounds = 17.76 + 0.84 × Sales - 1.29 × Month Diff: 2 Page Ref: 729 Section Heading: Regression Methods Keywords: multiple linear regression analysis AACSB: Analytical thinking

88) What are the salient performance statistics for the simple regression of Pounds on Sales? Provide an interpretation. Answer: The coefficient of determination for this equation is 0.922, which means that 92% of the variation in Pounds can be explained by the value of the independent variable Sales. The correlation between the two variables is 0.96, which is virtually a straight line. Diff: 2 Page Ref: 723 Section Heading: Regression Methods Keywords: regression methods AACSB: Analytical thinking

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89) What are the salient performance statistics for the simple regression model that predicts the level of Pounds by the number of the month the company is in (with January = 1)? Provide an interpretation. Answer: The coefficient of determination is 0.31, meaning that knowledge of the month can determine about 31% of the variation in the Pounds variable. The correlation coefficient between the two variables is -0.55, so as the month number increases, the level of Pounds decreases. Diff: 2 Page Ref: 723 Section Heading: Regression Methods Keywords: regression methods AACSB: Analytical thinking

The following data summarizes the historical demand for a product:

Month March April May June July August

Actual Demand 20 25 40 35 30 45

90) Use a four-period moving average to determine the forecasted demand for July, August, and September. Answer: July forecast = 30; August forecast = 32.5; September forecast = 37.5 Diff: 2 Page Ref: 704 Section Heading: Time Series Methods Keywords: moving avg method, forecast accuracy/error, MAPD, MAD, MSE AACSB: Analytical thinking

91) If the forecasted demand for June, July, and August is 32, 38 and 42, respectively, what is MAD? Answer: MAD = 4.67 Diff: 2 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: moving avg method, forecast accuracy/error, MAPD, MAD, MSE AACSB: Analytical thinking

92) If the forecasted demand for June, July, and August is 32, 38 and 42, respectively, what is MSE? Answer: MSE = 27.33 Diff: 2 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: moving avg method, forecast accuracy/error, MAPD, MAD, MSE AACSB: Analytical thinking

93) If the forecasted demand for June, July, and August is 32, 38 and 42, respectively, what is MAPD? Answer: MAPD = .127 or 12.7% Diff: 2 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: moving avg method, forecast accuracy/error, MAPD, MAD, MSE AACSB: Analytical thinking

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94) A manager uses the following equation to predict monthly receipts: Yt = 4,000 + 30t. What is the forecast for July of next year if t = 0 in April of this year? Answer: t = 15, so Yt = 4450 Diff: 2 Page Ref: 726 Section Heading: Regression Models Keywords: regression analysis AACSB: Analytical thinking

95) A local gym has discovered that their demand for personal trainers (measured in hours) is related not only to their own advertising expenditures in the prior month, but also to the demand for doughnuts and swim gear in the prior month at neighboring stores. The gym has developed the following regression model to forecast demand for personal trainers: Demand = 185 + (0.15 × advertising expenditures) - (0.05 × doughnuts) + (0.23 × swim gear sales) What is the forecast for October, given advertising expenditures of 1000, doughnut sales of 2450, and swim gear sales of 782 in September? Answer: 392.4 Diff: 2 Page Ref: 722 Section Heading: Time Series Forecasting Using Excel Keywords: multiple linear regression analysis AACSB: Analytical thinking

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The Taco Barn After tallying the receipts for their first year of operation, the owners of the Taco Barn are encouraged. Sales of their artisnal tacos, made from such exotic ingredients as ground beef, cheese, and beans, have been strong and seem to give hope to the coming year. Taco sales by month are shown in the table. Month January February March April May June July August September October November December

Sales 474 485 501 588 579 673 594 679 608 699 732 732

96) The manager is open to suggestions for forecasting models and decides to try both a linear trend model and a simple moving average of two periods. Generate forecasts for the year using these technique and then calculate forecast errors using MAD to determine which is the superior method in this scenario. Answer: The forecasts and their errors are indicated in the table: Month January February March April May June July August September October November December

Actual 474 485 501 588 579 673 594 679 608 699 719 732

Forecast MA

MAD MA

474 485 501 588 579 673 594 679 608 699 719

11 16 87 9 94 79 85 71 91 20 13

Forecast Trend 483 506 529 552 576 599 622 645 669 692 715 738

MAD Trend 9 21 28 36 3 74 28 35 61 7 4 6

The MAD for the Moving Average technique is a whopping 52, while the Trend has a MAD of 26, so trend would be the preferred approach. Diff: 3 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: MSE, mean squared error AACSB: Analytical thinking

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97) The manager is open to suggestions for forecasting models and decides to try both an exponential smoothing model with an alpha of 0.9 and a simple moving average of two periods. He decides to use the actual value for January as the forecast for February just to get the exponential smoothing forecasting party started. For the moving average approach, he uses the actual for January as the forecast for February and the actual for February as the forecast for March before beginning to apply the moving average equation. Generate forecasts for the year using these technique and then calculate forecast errors using MAD to determine which is the superior method in this scenario. Answer: The forecasts and their errors are indicated in the table: Month January February March April May June July August September October November December

Actual 474 485 501 588 579 673 594 679 608 699 719 732

Forecast MA

MAD MA

Forecast Expon

MAD Expon

474 485 501 588 579 673 594 679 608 699 719

11 16 87 9 94 79 85 71 91 20 13

474 484 499 579 579 664 601 671 614 691 716

11 17 89 0 94 70 78 63 85 28 16

The MAD for the Moving Average technique is a whopping 52, while the exponential smoothing has a MAD of 50.1, so exponential smoothing would be the preferred approach from an accuracy standpoint. Diff: 3 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: MSE, mean squared error AACSB: Analytical thinking

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98) The manager is open to suggestions for forecasting models and decides to try both an exponential smoothing model with an alpha of 0.9 and exponential smoothing with an alpha of 0.3. He decides to use the actual value for January as the forecast for February just to get the exponential smoothing forecasting party started. Generate forecasts for the year using these technique and then calculate forecast errors using MAD to determine which is the superior method in this scenario. Answer: The forecasts and their errors are indicated in the table: Month January February March April May June July August September October November December

Actual 474 485 501 588 579 673 594 679 608 699 719 732

Alpha=0.3

MAD 0.3

Alpha=0.9

MAD 0.9

474 477 484 515 534 576 581 611 610 637 661

11 24 96 64 139 18 98 3 89 82 71

474 484 499 579 579 664 601 671 614 691 716

11 17 89 0 94 70 78 63 85 28 16

The MAD for the exponential smooth with an alpha of 0.3 is a whopping 64, while the exponential smoothing has a MAD of 50.1, so the higher alpha exponential smoothing would be the preferred approach. Diff: 3 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: MSE, mean squared error AACSB: Analytical thinking

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99) The manager is open to suggestions for forecasting models. Plot the data and discuss the efficacy of the moving average, weighted moving average, exponential smoothing, and trend as the relate to this data. Answer: The plot appears below. The data exhibit a distinct upward trend. Running a trend line on the data yields a highly significant F statistic for the regression line (F=56.1, p<.001). There is the appearance of a cycle, stronger in the middle of the year than at the year's beginning or end.

If seasonal relatives are calculated on odd months and even months, the even relative is a 1.033 and the odd relative is 0.967. Plotting both a trend line and one with this seasonal adjustment reveals this.

The MAD for the trend line is 26 and the MAD for the adjusted trend line is marginally better at 23. Whether the Taco Barn has any reason to expect this type of cycle would be best left to the manager to explain, which would motivate choice of technique for the coming years. Diff: 3 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: MSE, mean squared error AACSB: Analytical thinking

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100) A ________ is a gradual, long-term, up-or-down movement of demand. A) seasonal pattern B) cycle C) trend D) prediction Answer: C Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: trend, forecasting components AACSB: Application of knowledge

101) A ________ is an up-and-down repetitive movement that repeats itself over a time span of more than 1 year. A) prediction B) seasonal pattern C) trend D) cyclical pattern Answer: D Diff: 1 Page Ref: 700 Section Heading: Forecasting Components Keywords: seasonal pattern AACSB: Application of knowledge

102) ________ methods are the most common type of forecasting method for the long-term strategic planning process. A) Regression B) Qualitative C) Time series D) Queuing Answer: B Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: qualitative methods AACSB: Application of knowledge

103) ________ is a category of statistical techniques that uses historical data to predict future behavior. A) Qualitative methods B) Regression C) Time series D) Quantitative methods Answer: C Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: time series analysis AACSB: Application of knowledge

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104) ________ use management judgment, expertise, and opinion to make forecasts. A) Qualitative methods B) Regression C) Time series D) Quantitative methods Answer: A Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: qualitative methods AACSB: Application of knowledge

105) The ________ is a procedure for developing a consensus forecast about what will occur in the future. A) Delphi method B) quantitative method C) regression equation D) time series forecasting method Answer: A Diff: 3 Page Ref: 703 Section Heading: Forecasting Components Keywords: Delphi method AACSB: Application of knowledge

106) ________ has become increasingly crucial to compete in the modern international business environment. A) The Delphi method B) Technological forecasting C) Prediction D) Exponential smoothing Answer: B Diff: 2 Page Ref: 703 Section Heading: Forecasting Components Keywords: technological forecasting AACSB: Application of knowledge

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107) Consider the following graph of sales.

Which of the following characteristics is exhibited by the data? A) trend only B) trend plus seasonal C) trend plus random D) none of the above Answer: D Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: forecasting components, trend, cyclical, seasonal AACSB: Application of knowledge

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108) Consider the following graph of sales.

Which of the following characteristics is exhibited by the data? A) trend only B) trend plus seasonal C) trend plus random D) seasonal only Answer: B Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: forecasting components, trend, random, seasonal AACSB: Application of knowledge

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109) Consider the following graph of sales.

Which of the following characteristics is exhibited by the data? A) trend only B) trend plus seasonal C) trend plus irregular D) seasonal Answer: C Diff: 2 Page Ref: 701 Section Heading: Forecasting Components Keywords: forecasting components, trend, seasonal, irregular AACSB: Application of knowledge

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Sales 474 485 501 588 579 673 594 679 608 699 732 732

110) Armed only with his fingers, the owner decides that the safest forecasting approach is a moving average of two periods. His fingers are aching by the time he reaches May and he is worried about his ability to stuff tacos during tomorrow's dinner rush. Help him out by finding the forecast for June. A) 583.5 B) 544.5 C) 626 D) 673 Answer: A Diff: 1 Page Ref: 704 Section Heading: Time Series Methods Keywords: moving average method AACSB: Analytical thinking

111) Armed only with his fingers, the owner decides that the safest forecasting approach is a weighted moving average using 0.6, 0.3, and 0.1 for the most recent three. His fingers are aching by the time he reaches May and he is worried about his ability to stuff tacos during tomorrow's dinner rush. Help him out by finding the forecast for June. A) 583.5 B) 573.9 C) 636.3 D) 673 Answer: B Diff: 2 Page Ref: 706 Section Heading: Time Series Methods Keywords: weighted moving average AACSB: Analytical thinking

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112) Armed only with his fingers, the owner decides that the safest forecasting approach is exponential smoothing with an alpha of 0.8. He uses the January demand and the January forecast just to get the ball rolling. His fingers are aching by the time he reaches March and he is worried about his ability to stuff tacos during tomorrow's dinner rush. Help him out by finding the forecast for April. A) 583.5 B) 482.8 C) 497.4 D) 588.0 Answer: C Diff: 3 Page Ref: 707 Section Heading: Time Series Methods Keywords: exponential smoothing AACSB: Analytical thinking

113) Armed only with his fingers, the owner decides that the safest forecasting approach is a linear trend line. His fingers are aching by the time he reaches May and he is worried about his ability to stuff tacos during tomorrow's dinner rush. Help him out by finding the forecast for June. A) 673.3 B) 628.2 C) 651.4 D) 599.3 Answer: D Diff: 3 Page Ref: 713 Section Heading: Time Series Methods Keywords: trend AACSB: Analytical thinking

114) Armed only with his fingers, the owner decides that the safest forecasting approach is a moving average of two periods. Generate a forecast for the year using this technique and then calculate forecast errors using MAD. What is the mean absolute deviation for this forecasting approach? A) 49.1 B) 44.5 C) 41.2 D) 43.3 Answer: A Diff: 2 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: Mean Absolute Deviation AACSB: Analytical thinking

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115) Armed only with his fingers, the owner decides that the safest forecasting approach is a weighted moving average using 0.6, 0.3, and 0.1 for the most recent three. Generate a forecast for the year using this technique and then calculate forecast errors using MAD. What is the mean absolute deviation for this forecasting approach? A) 53.3 B) 57.9 C) 63.6 D) 67.3 Answer: B Diff: 3 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: Mean Absolute Deviation AACSB: Analytical thinking

116) Armed only with his fingers, the owner decides that the safest forecasting approach is exponential smoothing with an alpha of 0.8. He uses the January demand and the January forecast just to get the ball rolling. Generate a forecast for the year using this technique and then calculate forecast errors using MAD. What is the mean absolute deviation for this forecasting approach? A) 41.3 B) 45.8 C) 49.9 D) 58.8 Answer: C Diff: 3 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: Mean Absolute Deviation AACSB: Analytical thinking

117) Armed only with his fingers, the owner decides that the safest forecasting approach is a linear trend line. Generate a forecast for the year using this technique and then calculate forecast errors using MAD. What is the mean absolute deviation for this forecasting approach? A) 33.3 B) 21.7 C) 28.2 D) 25.9 Answer: D Diff: 3 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: Mean Absolute Deviation AACSB: Analytical thinking

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118) Armed only with his fingers, the owner decides that the safest forecasting approach is a moving average of two periods. Generate a forecast for the year using this technique and then calculate forecast errors using MAPD. What is the mean absolute deviation for this forecasting approach? A) 7.67% B) 4.45% C) 6.24% D) 5.11% Answer: A Diff: 2 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: MAPD, forecast accuracy AACSB: Analytical thinking

119) Armed only with his fingers, the owner decides that the safest forecasting approach is a weighted moving average using 0.6, 0.3, and 0.1 for the most recent three. Generate a forecast for the year using this technique and then calculate forecast errors using MAPD. What is the mean absolute deviation for this forecasting approach? A) 5.33% B) 8.94% C) 6.36% D) 7.73% Answer: B Diff: 3 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: MAPD, forecast accuracy AACSB: Analytical thinking

120) Armed only with his fingers, the owner decides that the safest forecasting approach is exponential smoothing with an alpha of 0.8. He uses the January demand and the January forecast just to get the ball rolling. Generate a forecast for the year using this technique and then calculate forecast errors using MAPD. What is the mean absolute deviation for this forecasting approach? A) 4.13 B) 6.98% C) 7.85% D) 5.88% Answer: C Diff: 3 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: MAPD, forecast accuracy AACSB: Analytical thinking

33 .

121) Armed only with his fingers, the owner decides that the safest forecasting approach is a linear trend line. Generate a forecast for the year using this technique and then calculate forecast errors using MAPD. What is the mean absolute deviation for this forecasting approach? A) 3.33% B) 2.17% C) 2.82% D) 4.29% Answer: D Diff: 3 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: MAPD, forecast accuracy AACSB: Analytical thinking

122) Armed only with his fingers, the owner decides that the safest forecasting approach is a moving average of two periods. Generate a forecast for the year using this technique and then calculate forecast errors using MSE. What is the mean squared error for this forecasting approach? A) 3049 B) 4045 C) 6024 D) 5011 Answer: A Diff: 2 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: MSE, mean squared error AACSB: Analytical thinking

123) Armed only with his fingers, the owner decides that the safest forecasting approach is a weighted moving average using 0.6, 0.3, and 0.1 for the most recent three. Generate a forecast for the year using this technique and then calculate forecast errors using MSE. What is the mean squared error for this forecasting approach? A) 5033 B) 3960 C) 4036 D) 3466 Answer: B Diff: 3 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: MSE, mean squared error AACSB: Analytical thinking

34 .

124) Armed only with his fingers, the owner decides that the safest forecasting approach is exponential smoothing with an alpha of 0.8. He uses the January demand and the January forecast just to get the ball rolling. Generate a forecast for the year using this technique and then calculate forecast errors using MSE. What is the mean squared error for this forecasting approach? A) 4013 B) 3686 C) 3462 D) 3840 Answer: C Diff: 3 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: MSE, mean squared error AACSB: Analytical thinking

125) Armed only with his fingers, the owner decides that the safest forecasting approach is a linear trend line. Generate a forecast for the year using this technique and then calculate forecast errors using MSE. What is the mean squared error for this forecasting approach? A) 1033 B) 1217 C) 1282 D) 1148 Answer: D Diff: 3 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: MSE, mean squared error AACSB: Analytical thinking

126) ________ moving averages react more slowly to recent demand changes than do ________ moving averages. A) Longer-period, shorter-period B) Shorter-period, longer-period C) Longer-period, longer-period D) Shorter-period, shorter-period Answer: A Diff: 2 Page Ref: 705 Section Heading: Time Series Methods Keywords: moving averages, time series analysis AACSB: Application of knowledge

127) ________ are good for stable demand with no pronounced behavioral patterns. A) Longer-period moving averages B) Shorter-period moving averages C) Moving averages D) Weighted moving averages Answer: C Diff: 2 Page Ref: 703 Section Heading: Time Series Methods Keywords: moving averages, time series analysis AACSB: Application of knowledge

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128) ________ methods assume that what has occurred in the past will continue to occur in the future. A) Time series B) Regression C) Quantitative D) Qualitative Answer: A Diff: 2 Page Ref: 703 Section Heading: Time Series Methods Keywords: time series analysis AACSB: Application of knowledge

129) In exponential smoothing, the closer alpha is to ________, the greater the reaction to the most recent demand. A) -1 B) 0 C) 1 D) -1 or 1 Answer: C Diff: 2 Page Ref: 707 Section Heading: Time Series Methods Keywords: exponential smoothing AACSB: Application of knowledge

130) In adjusted exponential smoothing, the closer beta is to ________, the stronger a trend is reflected. A) -1 or 1 B) -1 C) 0 D) 1 Answer: D Diff: 2 Page Ref: 710 Section Heading: Time Series Methods Keywords: adjusted exponential smoothing AACSB: Application of knowledge

131) ________ is a linear regression model relating demand to time. A) Linear trend B) Linear regression C) Forecast demand D) Linear equation Answer: A Diff: 2 Page Ref: 713 Section Heading: Time Series Methods Keywords: linear regression model, regression analysis AACSB: Application of knowledge

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132) Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors? A) .01 B) .50 C) .90 D) 3.14 Answer: A Diff: 2 Page Ref: 707 Section Heading: Time Series Methods Keywords: simple exponential smoothing AACSB: Application of knowledge

133) Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing? A) 36.9 B) 57.5 C) 60.5 D) 62.5 Answer: D Diff: 2 Page Ref: 707 Section Heading: Time Series Methods Keywords: simple exponential smoothing AACSB: Analytical thinking

134) ________ is the difference between the forecast and actual demand. A) Forecast mistake B) Forecast error C) MAD D) Forecast accuracy Answer: B Diff: 2 Page Ref: 715 Section Heading: Forecast Accuracy Keywords: forecast error, forecast accuracy AACSB: Application of knowledge

135) ________ is absolute error as a percentage of demand. A) Cumulative error B) MAD C) MAPD D) Average error Answer: C Diff: 3 Page Ref: 717 Section Heading: Forecast Accuracy Keywords: MAPD, forecast accuracy AACSB: Application of knowledge

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136) ________ indicates a forecast is biased high. A) Large + B) Large C) Large : D) Large x Answer: B Diff: 2 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: cumulative error, average error AACSB: Analytical thinking

137) ________ is a measure of the strength of the relationship between independent variable(s) and a dependent variable. A) Correlation B) Linear regression C) Coefficient of determination D) Regression Answer: A Diff: 2 Page Ref: 725 Section Heading: Regression Methods Keywords: correlation, regression methods, linear regression model AACSB: Application of knowledge

138) ________ is the percentage of the variation in the dependent variable that results from the independent variable. A) Regression B) Coefficient of determination C) Correlation D) Linear regression Answer: B Diff: 2 Page Ref: 726 Section Heading: Regression Methods Keywords: coefficient of determination, reg methods, linear reg model AACSB: Application of knowledge

139) Coefficient of determination is the percentage of the variation in the ________ variable that results from the ________ variable. A) dependent, dependent B) independent, dependent C) dependent, independent D) independent, independent Answer: C Diff: 3 Page Ref: 726 Section Heading: Regression Methods Keywords: coefficient of determination, linear reg model, reg methods AACSB: Application of knowledge

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140) Consider the following demand and forecast. Period 1 2 3 4

Demand 7 12 18 22

Forecast 10 15 20

If MAD = 2 for the four periods under consideration, what is the forecast for period 4? A) 19 B) 20 C) 21 D) 22 Answer: D Diff: 2 Page Ref: 709 Section Heading: Forecast Accuracy Keywords: forecast error, MAD AACSB: Analytical thinking

Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

141) Use a 2-period moving average to forecast demand for period 7. A) 227.5 B) 275 C) 280 D) 290 Answer: D Diff: 2 Page Ref: 704 Section Heading: Time Series Methods Keywords: moving average method AACSB: Analytical thinking

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142) Use a 3-period moving average to forecast demand for period 7. A) 283.33 B) 280 C) 290 D) 310 Answer: A Diff: 2 Page Ref: 704 Section Heading: Time Series Methods Keywords: moving average method AACSB: Analytical thinking

143) If the forecast for period 5 is equal to 275, use exponential smoothing to compute a forecast for period 7 if α = .40. A) 273 B) 277 C) 267.8 D) 286.2 Answer: D Diff: 2 Page Ref: 707 Section Heading: Time Series Methods Keywords: exponential smoothing AACSB: Analytical thinking

The following data represents quarterly sales of lawnmowers. Year 1 2

Quarter 1 150 160

Quarter 2 140 148

Quarter 3 190 210

Quarter 4 165 175

144) What is the seasonal index for the third quarter? (Round to the nearest hundredth.) A) .20 B) .22 C) .26 D) .30 Answer: D Diff: 2 Page Ref: 707 Section Heading: Forecasting Components Keywords: seasonal factors AACSB: Analytical thinking

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145) What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.) A) .20 B) .23 C) .25 D) .30 Answer: C Diff: 2 Page Ref: 707 Section Heading: Forecasting Components Keywords: seasonal factors AACSB: Analytical thinking

146) The manager of "Skis 4 U" is preparing a forecast for February of 2010. Demand exhibits both trend and seasonality. The trend equation for monthly demand is y = 4375 + 80t, where t = 1 for January 2009. The seasonal index for February is 1.25. The forecast for February is: A) 4575. B) 4583. C) 5668. D) 6769. Answer: D Diff: 2 Page Ref: 707 Section Heading: Time Series Methods Keywords: seasonal factors AACSB: Analytical thinking

147) Given forecast errors of 6, 4, 0 and -2, what is the mean absolute deviation? A) 2 B) 3 C) 4 D) 2.67 E) none of the above Answer: B Diff: 2 Page Ref: 716 Section Heading: Forecast Accuracy Keywords: forecast error, MAD AACSB: Analytical thinking

148) Given forecast errors of 6, 4, 0 and -2, what is the mean squared error? A) 14 B) 18.67 C) 16 D) 12 E) none of the above Answer: A Diff: 2 Page Ref: 718 Section Heading: Forecast Accuracy Keywords: forecast error, MSE AACSB: Analytical thinking

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Sales 45 57 32 44 51 34

Pounds 54.3 63.8 39.5 49.8 52.3 39.9

149) What is a three-period moving average forecast for the month of July? A) 47.33 B) 46.10 C) 45.38 D) 44.29 Answer: A Diff: 2 Page Ref: 704 Section Heading: Time Series Methods Keywords: moving averages AACSB: Analytical thinking

150) What is the three-period weighted moving average for July using the weights 0.5 (most recent), 0.3, and 0.2? A) 48.99 B) 45.6 C) 49.51 D) 46.09 Answer: B Diff: 2 Page Ref: 706 Section Heading: Time Series Methods Keywords: weighted moving average method AACSB: Analytical thinking

151) Using 1 to represent January, 2 to represent February, and so on, what is the intercept for the regression equation that predicts the pounds of supplies available? A) 0.55 B) -2.74 C) 59.55 D) 8.87 Answer: C Diff: 2 Page Ref: 725 Section Heading: Regression Methods Keywords: regression analysis AACSB: Analytical thinking

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152) What is the forecast for July if exponential smoothing with an alpha=.04 generated a forecast of 43.0 for June? A) 41.25 B) 40.64 C) 43.16 D) 42.88 Answer: D Diff: 2 Page Ref: 707 Section Heading: Time Series Methods Keywords: exponential smoothing AACSB: Analytical thinking

153) What is the slope of the regression equation developed when the Sales data are used to predict the Pounds? A) 0.92 B) 0.86 C) 0.80 D) 0.71 Answer: A Diff: 2 Page Ref: 725 Section Heading: Regression Methods Keywords: linear regression AACSB: Analytical thinking

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Introduction to Management Science, 12e (Taylor) Chapter 16 Inventory Management 1) Independent demand items are used internally to produce a final product. Answer: FALSE Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: dependent demand items AACSB: Application of knowledge

2) Dependent demand items are final products demanded by an external customer. Answer: FALSE Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: independent demand items AACSB: Application of knowledge

3) Inventory costs include carrying, ordering, and shortage costs. Answer: TRUE Diff: 1 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: inventory costs AACSB: Application of knowledge

4) The purpose of inventory management is to determine how much and when to order. Answer: TRUE Diff: 1 Page Ref: 769 Section Heading: Elements of Inventory Management Keywords: inventory management AACSB: Application of knowledge

5) In a continuous inventory system, a constant amount is ordered when inventory declines to a predetermined level. Answer: TRUE Diff: 2 Page Ref: 769 Section Heading: Inventory Control Systems Keywords: inventory control systems, continuous inventory system AACSB: Application of knowledge

6) In a periodic inventory system, a constant amount is ordered when inventory declines to a predetermined level. Answer: FALSE Diff: 2 Page Ref: 770 Section Heading: Inventory Control Systems Keywords: continuous inventory system AACSB: Application of knowledge

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7) The EOQ is the optimal order quantity that will minimize total carrying costs. Answer: FALSE Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: economic order quantity models, EOQ models AACSB: Application of knowledge

8) Assumptions of the basic EOQ model include constant demand, no shortages, constant lead time, and instantaneous replenishment. Answer: TRUE Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: economic order quantity models, EOQ models AACSB: Application of knowledge

9) The noninstantaneous receipt model applies only to manufacturing. Answer: FALSE Diff: 3 Page Ref: 776 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: EOQ Model with noninstantaneous receipt AACSB: Application of knowledge

10) The EOQ model with shortages does not allow backorders. Answer: FALSE Diff: 3 Page Ref: 769 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages AACSB: Application of knowledge

11) The basic EOQ model plays no role in determining order sizes in the presence of quantity discounts. Answer: FALSE Diff: 2 Page Ref: 784 Section Heading: Quantity Discounts Keywords: EOQ model quantity discounts AACSB: Application of knowledge

12) Quantity discounts are always evaluated with carrying cost as a percentage of price. Answer: FALSE Diff: 2 Page Ref: 785 Section Heading: Quantity Discounts Keywords: EOQ model quantity discounts AACSB: Application of knowledge

13) The service level is the probability that the inventory available during lead time will meet demand. Answer: TRUE Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: service level, safety stocks AACSB: Application of knowledge

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14) If service level is 50%, then safety stock is equal to 50% of lead time demand. Answer: FALSE Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: safety stock, service level AACSB: Application of knowledge

15) The reorder point is the date when a new order should be placed. Answer: FALSE Diff: 1 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point AACSB: Application of knowledge

16) If lead time and demand are constant, safety stock is equal to demand multiplied by lead time. Answer: FALSE Diff: 1 Page Ref: 789 Section Heading: Reorder Point Keywords: safety stock AACSB: Analytical thinking

17) Periodic inventory systems normally require smaller safety stock than a continuous inventory system. Answer: FALSE Diff: 2 Page Ref: 793 Section Heading: Order Quantity for a Periodic Inventory System Keywords: periodic inventory system AACSB: Application of knowledge

18) A periodic inventory system has constant order sizes and order intervals. Answer: FALSE Diff: 2 Page Ref: 793 Section Heading: Order Quantity for a Periodic Inventory System Keywords: periodic inventory system, fixed time period inventory system AACSB: Application of knowledge

19) If all of the assumptions for the basic EOQ model are met, the fixed-period model will behave exactly like the EOQ model. Answer: TRUE Diff: 2 Page Ref: 793 Section Heading: Order Quantity for a Periodic Inventory System Keywords: periodic inventory system, fixed time period inventory system AACSB: Analytical thinking

20) Carrying costs include storage cost, interest, and depreciation. Answer: TRUE Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: inventory costs AACSB: Application of knowledge

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21) Ordering costs include transportation, shipping, and inspection. Answer: TRUE Diff: 2 Page Ref: 768 Section Heading: Elements of Inventory Management Keywords: inventory costs AACSB: Application of knowledge

22) Shortage costs include loss of customer goodwill. Answer: TRUE Diff: 2 Page Ref: 769 Section Heading: Elements of Inventory Management Keywords: inventory costs AACSB: Application of knowledge

23) If a business frequently runs out of inventory, their service levels are negative. Answer: FALSE Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: service level AACSB: Analytical thinking

24) The service level is the probability that the inventory available during the lead time will meet the demand. Answer: TRUE Diff: 1 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: service level, safety stocks AACSB: Application of knowledge

25) The lower the service level, the greater the probability of a stockout. Answer: TRUE Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: service level, safety stocks AACSB: Analytical thinking

26) Service level is positively correlated with the size of the buffer stock. Answer: TRUE Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: service level, safety stocks AACSB: Analytical thinking

27) ________ demand items are generally final products demanded by customers. Answer: Independent Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: independent demand items AACSB: Application of knowledge

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28) The purpose of inventory management is to determine ________ and ________ to order. Answer: how much, when Diff: 2 Page Ref: 769 Section Heading: Elements of Inventory Management Keywords: inventory management AACSB: Application of knowledge

29) ________ demand items are used internally to produce a final product. Answer: Dependent Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: independent demand items AACSB: Application of knowledge

30) Inventory ________ costs include storage cost and the cost of capital. Answer: carrying Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: carrying cost AACSB: Application of knowledge

31) Inventory ________ costs include transportation and inspection. Answer: ordering Diff: 2 Page Ref: 768 Section Heading: Elements of Inventory Management Keywords: ordering costs AACSB: Application of knowledge

32) A ________ occurs when customer demand cannot be met and the sale is lost because of insufficient inventory. Answer: shortage or stock out Diff: 2 Page Ref: 779 Section Heading: The EOQ Model with Shortages Keywords: shortage or stock out costs AACSB: Application of knowledge

33) In a ________ inventory system, a constant amount is ordered when inventory declines to a predetermined level. Answer: continuous Diff: 2 Page Ref: 769 Section Heading: Inventory Control Systems Keywords: continuous inventory system AACSB: Application of knowledge

34) In a ________ inventory system, an order is placed for a variable amount after a fixed passage of time. Answer: periodic Diff: 2 Page Ref: 770 Section Heading: Inventory Control Systems Keywords: periodic inventory system AACSB: Application of knowledge

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35) ________ is the optimal order quantity that will minimize the total inventory costs. Answer: EOQ or economic order quantity Diff: 1 Page Ref: 771 Section Heading: Economic Order Quantity Models Keywords: economic order quantity, EOQ AACSB: Application of knowledge

36) A ________ occurs when an item is out of stock and is sold to the customer when a shipment arrives. Answer: backorder Diff: 2 Page Ref: 779 Section Heading: The EOQ Model with Shortages Keywords: economic order quantity model, EOQ model assumptions AACSB: Application of knowledge

37) Costs involved in a typical inventory model include ________ and ________. Answer: carrying costs, ordering costs Diff: 1 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: EOQ model, average inventory AACSB: Application of knowledge

38) In the basic EOQ model, as the size of the order increases, the annual ________ cost decreases. Answer: ordering Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: economic order quantity model inventory costs, ordering costs AACSB: Application of knowledge

39) In the basic EOQ model, the amount ordered is received in ________ shipment(s). Answer: one Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: economic order quantity model AACSB: Application of knowledge

40) The objective of the basic EOQ model is to ________. Answer: minimize costs Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: economic order quantity model AACSB: Application of knowledge

41) In the basic EOQ model, as the size of the order increases, the annual ________ cost increases. Answer: carrying Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: economic order quantity model, inventory costs, carrying costs AACSB: Application of knowledge

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42) In the quantity discounts model, the ________ must be included in the total cost calculation. This variable is not included in the basic EOQ model. Answer: purchase price Diff: 2 Page Ref: 784 Section Heading: Quantity Discounts Keywords: quantity discounts AACSB: Application of knowledge

43) If all the variables are held constant, the total inventory cost in a noninstantaneous receipts model is ________ than the total cost in the basic EOQ model. Answer: larger or higher Diff: 3 Page Ref: 776 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: production lot size model, non-instantaneous receipts model AACSB: Application of knowledge

44) The ________ determines when an order should be placed for a continuous review inventory system. Answer: reorder point Diff: 1 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point AACSB: Application of knowledge

45) The reorder point will ________ if lead time increases and demand per day remains the same. Answer: increase Diff: 1 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point, safety stock, service level AACSB: Application of knowledge

46) If demand per day or lead time are not constant, then the reorder point must include a level of inventory called ________. Answer: safety stock Diff: 1 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point, safety stock, service level AACSB: Application of knowledge

47) When viewing a plot of inventory level against time, the distance on the time axis from when an order has been placed to when it is received is ________. Answer: lead time Diff: 1 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point, safety stock, service level AACSB: Application of knowledge

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48) ________ is inventory that is used to help protect against stockouts. Answer: Safety stock Diff: 1 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: safety stock AACSB: Application of knowledge

49) ________ is the probability that the inventory available during the lead time will meet demand. Answer: Service level Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: service level AACSB: Application of knowledge

50) If lead time and demand are constant then ________ is zero. Answer: safety stock Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: safety stock AACSB: Analytical thinking

51) For the ________ inventory system, Q, the quantity ordered, can vary. Answer: periodic Diff: 2 Page Ref: 770 Section Heading: Inventory Control Systems Keywords: periodic inventory system AACSB: Application of knowledge

52) The EOQ model is ________ , or resistant to errors in the cost estimates and demand. Answer: robust Diff: 2 Page Ref: 774 Section Heading: Economic Order Quantity Models Keywords: economic order quantity, EOQ AACSB: Application of knowledge

53) ________ costs and ________ costs react inversely to each other in response to an increase in order size. Answer: Carrying, ordering Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: inventory costs AACSB: Application of knowledge

54) The basic EOQ model assumes that ________ is known with certainty and is relatively constant over time. Answer: demand Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: EOQ model, econ order quantity models, assumption of EOQ models AACSB: Application of knowledge

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55) In the basic EOQ model, if D = 80 per month, C o = $13, and Cc = $11 per unit per month, what is the EOQ? Answer: 13.75 Diff: 1 Page Ref: 775 Section Heading: Economic Order Quantity Models Keywords: EOQ model, economic order quantity models AACSB: Analytical thinking

56) In the basic EOQ model, if D = 40 per month, C o = $9, and Cc = $8 per unit per month, what is the EOQ? Answer: 9.49 Diff: 1 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity models AACSB: Analytical thinking

57) In the basic EOQ model, if D = 100 per month, Co = $20, and Cc = $15 per unit per month, what is the EOQ? Answer: 16.33 Diff: 1 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity models AACSB: Analytical thinking

58) In the basic EOQ model, if annual demand is 50 units, carrying cost is $2 per unit per year, and ordering cost is $15, what is the EOQ? Answer: 27.39 Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity models AACSB: Analytical thinking

A company produces item Y, and uses the basic EOQ model for managing its inventory. Lead time to obtain item Y is two weeks. Demand is normally distributed with a mean of 400 units per week and a standard deviation of 40 units per week. The desired service level is 98.5%. The ordering cost is $20, and carrying cost is 20% of the items cost, which is $10. 59) Determine the order quantity for product Y. (Assume 52 weeks of operation per year.) Answer: 644.98 Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: economic order quantity model, EOQ model AACSB: Analytical thinking

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60) Determine the annual setup cost and the annual carrying cost for product Y for the economic order quantity. (Assume 52 weeks of operation per year.) Answer: $1289.96 for both; $644.98 each Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: the annual setup cost, economic order quantity models AACSB: Analytical thinking

61) Determine the total annual inventory cost for product Y. Include the item cost in your calculations. (Assume 52 weeks of operation per year.) Answer: $209,290 Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: the annual setup cost, economic order quantity models AACSB: Analytical thinking

62) Determine the reorder point for product Y. Answer: 922.75 Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: economic order quantity models, reorder point AACSB: Analytical thinking

Kushie's Coffee in Bangalore is a quaint establishment nestled near MG Road in the central business district. It serves coffee and fruit cake to a clientele that has been enjoying these products for over fifty years. The demand for coffee beans is 6600 cases per year (each case has 24 ten-pound bags). It would be disastrous for them to run out of coffee, so they keep a safety stock of 30 cases. The cases cost $4800 and it costs $5 per case to order coffee. As coffee is a perishable product, the holding cost is fairly high at $40/case/year. The lead time to receive an order is seven days. Kushie's is open 300 days a year. 63) What is the optimal order quantity for Kushie's Coffee? Answer: 40.62 cases Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

64) How many orders per year does Kushie's place if they order a cost minimizing quantity? Answer: 162.48 orders/year Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

65) What is their cost for holding all types of inventory if they order optimally? Answer: Annual holding cost (812.4) plus holding safety stock (1200) comes to $2012.40. Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

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66) What is their total policy cost (including cost of goods) if they order at the EOQ amount? Answer: $31,682,820. Wow, you'd never guess it was that high if you saw this place! Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

67) What is the reorder point for Kushie's if they reorder a quantity twice as high as their EOQ? Answer: 184 units Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

The injection molding department of Alver Inc. uses an average of 40 pounds of a special powder per day. The plant operates 250 days per year. The daily usage of the powder is normally distributed with a standard deviation of 5 pounds per day. The lead time to obtain the powder from a supplier is 9 days. The annual holding cost is $2 per unit and the cost of ordering the powder is $50. 68) How many units should Alver Inc. order in order to minimize annual ordering and carrying cost? Answer: 707.11 Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: economic order quantity AACSB: Analytical thinking

69) How many orders will be placed each year? Answer: 14.14 orders Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: economic order quantity model, number of orders AACSB: Analytical thinking

70) Determine the reorder point for a service level of 97%. Answer: 388.2 units Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: reorder point, service level AACSB: Analytical thinking

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The daily sales of a peanut butter at Power's Grocery are normally distributed, with a mean of 12 jars and a standard deviation of 4. The manager checks the inventories on shelves and places an order every three days. Delivery lead time is two days. 71) How much safety stock of peanut butter should they have for a 99% service level? Answer: Z = 2.33, r = 3, and L = 2 SS = 2.33 (4)(5)1/2 = 20.8 or 21 jars Diff: 2 Page Ref: 791 Section Heading: Determining Safety Stocks Using Service Levels Keywords: payoff table AACSB: Analytical thinking

72) If there are four jars on the shelf when an order is placed, how much should the store order? Answer: Base stock level =

(tb + L) + safety stock = 12(5) + 21 = 60 + 21 = 81.

Order quantity = 81 - 4 = 77 jars. Diff: 2 Page Ref: 793 Section Heading: Order Quantity for a Periodic Inventory System Keywords: payoff table AACSB: Analytical thinking

73) The daily demand for a product is normally distributed with a mean of 80 and a standard deviation of 8. Constant lead time is 4 days. The cost of placing an order is $20. The item costs $8 and the carrying rate per year is 10% of the item cost. Determine the economic order quantity for a 365-day year. Answer: 1209 Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: economic order quantity AACSB: Analytical thinking

74) In a noninstantaneous receipt model, daily demand is 55 units and daily production is 120 units, C o = $70 and Cc = $4 per unit/year. The production facility operates 300 days per year. What is the maximum inventory level? Answer: 559.3 units Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: EOQ Model with noninstantaneous receipt AACSB: Analytical thinking

75) In a noninstantaneous receipt model, daily demand is 55 units and daily production is 120 units, C o = $70 and Cc = $4 per unit/year. The production facility operates 300 days per year. What is the optimal order quantity? Answer: 1032.55 Diff: 1 Page Ref: 778 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: noninstantaneous receipt model, economic production model AACSB: Analytical thinking

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76) A product has an annual demand of 3600 units. Unit cost for this product is $3. Set up cost is $20 and the inventory carrying rate as a percent of the unit cost is 25%. The product is produced in-house where the daily production rate is 50 units. Assume 360 working days per year and determine the economic production quantity. Answer: 490 units Diff: 2 Page Ref: 778 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: econ order/prod quantity, non-instantaneous receipts model AACSB: Analytical thinking

77) A product has an annual demand of 3600 units. Unit cost for this product is $3. Set up cost is $20 and the inventory carrying rate as a percent of the unit cost is 25%. The product is produced in-house where the daily production rate is 50 units. Assume 360 working days per year. Determine the annual ordering cost and carrying cost if the optimal production quantity is made each time. Answer: $147 and $147 for a total of $294. Diff: 2 Page Ref: 767 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: econ order/prod quant, non-instant receipt mod, an order/carry cost AACSB: Analytical thinking

78) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year and CS = $25, what is the total annual shortage cost? Answer: 296.53 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the total annual shortage cost AACSB: Analytical thinking

79) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year and CS = $25, what is the optimal order quantity? Answer: Qopt = 495.74 units Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the optimal order quantity AACSB: Analytical thinking

80) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year and CS = $25, what is the annual ordering cost? Answer: 1355.54 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: the annual ordering cost, EOQ model with shortages AACSB: Analytical thinking

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81) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year and CS = $25, what is the optimal stock out level? Answer: Sopt = 108.44 units Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: optimal stock out level, EOQ model with shortages AACSB: Analytical thinking

82) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year and CS = $25, what is the annual carrying cost? Answer: 1059.03 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: the annual carrying cost, EOQ model with shortages AACSB: Analytical thinking

83) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year and CS = $25, what is the total minimum annual inventory cost? Answer: TCmin = 2711.09 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: total minimum annual inventory cost, EOQ model with shortages AACSB: Analytical thinking

A company distributes repair parts for high-end appliances. The annual demand is 81,000 and the company operates 300 days per year. The annual carrying cost is 20% of the item cost, which is $500. The ordering cost is estimated at $60 and the shortage cost is $150. 84) Determine the optimal order quantity. Answer: 402.5 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages AACSB: Analytical thinking

85) Determine the optimal shortage level. Answer: 161 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the optimal shortage level AACSB: Analytical thinking

86) How many order per year will they place? Answer: 201 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the annual carrying cost AACSB: Analytical thinking

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87) What is the maximum inventory level? Answer: 242 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the annual setup cost AACSB: Analytical thinking

88) Determine the annual shortage cost. Answer: $4830 Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the annual shortage cost AACSB: Analytical thinking

89) If the daily demand is 30 and the lead time in days is 3, what is the reorder point? Answer: 90 Diff: 1 Page Ref: 789 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

90) If the daily demand is 67 and the lead time in days is 2, what is the reorder point? Answer: 134 Diff: 1 Page Ref: 789 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

91) If the daily demand is 25 and the lead time in days is 4, what is the reorder point? Answer: 100 Diff: 1 Page Ref: 789 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

92) Sonny Lawler's law office uses EOQ models to manage their office supplies. They've been ordering ink refills for their printers in quantities of 60 units. The firm estimates carrying cost at 40% of the $10 unit cost and that annual demand is about 240 units per year. The assumptions of the basic EOQ model are thought to apply. For what value of ordering cost would its action be optimal? Answer: $30 Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: economic order quantity AACSB: Analytical thinking

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93) Dana Swor's Dream Store sells weight loss products. Her best-selling item, an energy booster and fat burning pill, has an annual demand of 400 units. Ordering cost is $40 and carrying cost is $5 per unit year. How many units should she order to minimize total inventory costs? Answer: 80 Diff: 1 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

94) Annual demand for a paperback dictionary at the bookstore is 1200 units. Ordering costs are 350, carrying costs are $6 per unit per year, and the lead time is 9 days. The bookstore is open for 300 days of the year. What is the reorder point? Answer: 36 Diff: 1 Page Ref: 789 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

95) If average demand for an inventory item is 200 units per day, lead time is 3 days, and safety stock is 100 units, what is the reorder point? Answer: 700 Diff: 1 Page Ref: 789 Section Heading: Reorder Point Keywords: safety stock, reorder point AACSB: Analytical thinking

96) If average demand for an inventory item is 180 units per day, lead time is 5 days, and safety stock is 90 units, what is the reorder point? Answer: 990 Diff: 1 Page Ref: 789 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

97) Annual demand for notecards at Suzie's Stationery shop is 10,000 units. Deliveries take about 5 working days and Suzie operates 300 days per year. Calculate the reorder point for the notecards that she stocks. Answer: 167 notecards = 33.33 × 5 Diff: 1 Page Ref: 789 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

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A bakery uses an average of 60 ounces of organic orange juice daily. Demand is normally distributed with a standard deviation of 15 ounces. The bakery places orders every seven days. The lead time for delivery of the juice is three days. 98) Compute the safety stock required to achieve a 98% service level. Answer: 97 ounces Diff: 1 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: periodic inventory system AACSB: Analytical thinking

99) If the bakery has 190 ounces at the time an order is placed, how much should be ordered? Answer: 697 - 190 = 507 ounces Diff: 2 Page Ref: 793 Section Heading: Order Quantity for a Periodic Inventory System Keywords: periodic inventory system AACSB: Analytical thinking

100) The daily demand for a product is normally distributed with a mean of 80 and a standard deviation of 8. Constant lead time is 4 days. The cost of placing an order is $20. The item costs $8 and the carrying rate per year is 10% of the item cost. Determine the reorder point to satisfy 90% of the orders. Answer: 340.48 Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: economic order quantity, reorder point AACSB: Analytical thinking

101) A bakery's use of corn syrup is normally distributed with a mean of 50 gallons per day and a standard deviation of 5 gallons per day. Lead time for delivery of the syrup is normal with a mean of 4 days and a standard deviation of 2 days. The manager wants a service level of 99 percent. Calculate the reorder point. Answer: 434 gallons Diff: 3 Page Ref: 792 Section Heading: Determining Safety Stocks Using Service Levels Keywords: reorder point, variable demand, variable lead time AACSB: Analytical thinking

102) A bakery's use of corn syrup is normally distributed with a mean of 50 gallons per day and a standard deviation of 5 gallons per day. Lead time for delivery of the syrup is normal with a mean of 4 days and a standard deviation of 2 days. The manager reorders when his inventory drops to 300 gallons. What cycle service level is implied by this policy? Answer: z = .995, so service level = 84% Diff: 3 Page Ref: 792 Section Heading: Determining Safety Stocks Using Service Levels Keywords: reorder point, variable demand/lead time, service level AACSB: Analytical thinking

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103) A manager has just received a revised price schedule from a vendor. What order quantity should the manager use in order to minimize total costs? Annual demand is 120 units, ordering cost is $10, and annual carrying cost is $1 per unit. Quantity 1-59 60-99 100 or more

Unit Price $15 $14 $13

Answer: Optimal Q = 49. TC(49) = $1849; TC(60) = $1730; TC (100) = $1622, so order 100. Diff: 3 Page Ref: 784 Section Heading: Quantity Discounts Keywords: quantity discounts, constant carrying cost per unit AACSB: Analytical thinking

104) An office manager uses 400 boxes of file folders per year. The price is $8.50 per box for an order size of 199 boxes or less, $8.00 per box for orders of 200 to 799 boxes, and $7.50 per box for an order of 800 or more boxes. Carrying cost is 20 percent of the price of the product and ordering costs are $80. What order quantity minimizes total annual cost? Answer: Optimal Q = 194. TC(194) = $3730; TC(200) = $3520; TC(800) = $3640, so order 200. Diff: 3 Page Ref: 784 Section Heading: Quantity Discounts Keywords: quantity discounts AACSB: Analytical thinking

105) ________ demand items are used internally to produce a final product. A) Independent B) Dependent C) Assumed D) Internal Answer: B Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: inventory management AACSB: Application of knowledge

106) ________ demand items are final products demanded by an external customer. A) Dependent B) Independent C) External D) Integrated Answer: B Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: independent demand AACSB: Application of knowledge

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107) Inventory costs include: A) carrying costs. B) ordering costs. C) shortage costs. D) all of the above Answer: D Diff: 2 Page Ref: 767 Section Heading: Elements of Inventory Management Keywords: inventory costs AACSB: Application of knowledge

108) The purpose of inventory management is to determine: A) timing and cost of orders. B) quantity and cost of orders. C) timing and quantity of orders. D) ordering and carrying costs. Answer: C Diff: 2 Page Ref: 769 Section Heading: Elements of Inventory Management Keywords: inventory management AACSB: Application of knowledge

109) A keyboard costs $1000, and the annual holding cost is 25%. Annual demand is 10,000 units, and the order cost is $150 per order. What is the approximate economic order quantity? A) 16 B) 70 C) 110 D) 183 Answer: C Diff: 3 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: economic order quantity, EOQ AACSB: Analytical thinking

110) In a(n) ________ inventory system, a constant amount is ordered when inventory declines to a predetermined level. A) optimal B) economic C) periodic D) continuous Answer: D Diff: 2 Page Ref: 769 Section Heading: Inventory Control Systems Keywords: continuous inventory system AACSB: Application of knowledge

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111) In a(n) ________ inventory system, an order is placed for a variable amount after a fixed passage of time. A) periodic B) continuous C) optimal D) economic Answer: A Diff: 2 Page Ref: 770 Section Heading: Inventory Control Systems Keywords: periodic inventory system AACSB: Application of knowledge

112) EOQ is used in a(n) ________ inventory system. A) periodic B) continuous C) optimal D) economic Answer: B Diff: 3 Page Ref: 769 Section Heading: Economic Order Quantity Models Keywords: economic order quantity models, EOQ models AACSB: Application of knowledge

113) EOQ is the optimal order quantity that will ________ total inventory costs. A) maximize B) minimize C) steady D) maintain Answer: B Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity models AACSB: Application of knowledge

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Kushie's Coffee in Bangalore is a quaint establishment nestled near MG Road in the central business district. It serves coffee and fruit cake to a clientele that has been enjoying these products for over fifty years. The demand for coffee beans is 6600 cases per year (each case has 24 ten-pound bags). It would be disastrous for them to run out of coffee, so they keep a safety stock of 30 cases. The cases cost $4800 and it costs $5 per case to order coffee. As coffee is a perishable product, the holding cost is fairly high at $40/case/year. The lead time to receive an order is seven days. Kushie's is open 300 days a year. 114) What is their economic order quantity? A) 40.6 cases B) 162.5 cases C) 406 cases D) 1649.9 cases Answer: A Diff: 2 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: economic order quantity model AACSB: Analytical thinking

115) How many orders per year do they place if they order at double their EOQ quantity? A) 40.6 B) 81.2 C) 162.5 D) 325 Answer: B Diff: 2 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: economic order quantity model AACSB: Analytical thinking

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The Krewe of Orpheus The Krewe of Orpheus maintains a supply of swizzle sticks for events throughout the year. Demand for swizzle sticks is shockingly low, a quick check of krewe records from last year reveals that they used only 585,000, but the krewe president believes that they should be good stewards of what they have, so they seek to manage this inventory using the EOQ policy, although they prefer to refer to it as an EOKrewe policy for obvious reasons. Swizzle sticks are not expensive items, they cost a nickel apiece largely due to the club logo printed on each one. This also serves to increase the lead time as they can't be obtained from a standard restaurant supply house. Instead, they must be ordered with an eye towards the six day lead time. It costs $15 to place an order, most of this cost is a result of explaining the meaning of "Laissez les bons temps rouler" and why it should be printed on the edge of each swizzle stick. Holding cost is 20% of purchase price. 116) The supplier offers the Krewe of Orpheus a deal; if they will buy at least 50,001 at a time, they will pay only 4 cents each, and if they buy at least 100,001 at a time, they will pay only 3 cents each. What is the optimal order quantity? A) 41,892 B) 46,837 C) 50,001 D) 100,001 Answer: D Diff: 3 Page Ref: 785 Section Heading: Quantity Discounts Keywords: quantity discounts AACSB: Analytical thinking

117) The supplier offers the Krewe of Orpheus a deal; if they will buy at least 50,000 at a time, they will pay only 4.9 cents each, and if they buy at least 100,000 at a time, they will pay only 4.8 cents each. What is the total cost of the optimal order quantity? A) $29,668.93 B) $28,822.32 C) $28,647.75 D) $29,085.50 Answer: C Diff: 3 Page Ref: 785 Section Heading: Quantity Discounts Keywords: quantity discounts AACSB: Analytical thinking

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118) The supplier offers the Krewe of Orpheus a deal; if they will buy at least 50,000 at a time, they will pay only 4.99 cents each, and if they buy at least 100,000 at a time, they will pay only 4.98 cents each. What is the optimal order quantity? A) 41,892 B) 46,837 C) 50,000 D) 100,000 Answer: C Diff: 3 Page Ref: 785 Section Heading: Quantity Discounts Keywords: quantity discounts AACSB: Analytical thinking

119) The supplier offers the Krewe of Orpheus a deal; if they will buy at least 50,000 at a time, they will pay only 4.99 cents each, and if they buy at least 100,000 at a time, they will pay only 4.98 cents each. What is the total cost arising from the optimal order quantity? A) $29,521.78 B) $29,616.50 C) $29,668.93 D) $29,718.75 Answer: B Diff: 3 Page Ref: 785 Section Heading: Quantity Discounts Keywords: quantity discounts AACSB: Analytical thinking

Kushie's Coffee in Bangalore is a quaint establishment nestled near MG Road in the central business district. It serves coffee and fruit cake to a clientele that has been enjoying these products for over fifty years. The demand for coffee beans is 6600 cases per year (each case has 24 ten-pound bags). It would be disastrous for them to run out of coffee, so they keep a safety stock of 30 cases. The cases cost $4800 and it costs $5 per case to order coffee. As coffee is a perishable product, the holding cost is fairly high at $40/case/year. The lead time to receive an order is seven days. Kushie's is open 300 days a year. 120) What is their reorder point if they order at twice their EOQ? A) 46 cases B) 92 cases C) 184 cases D) 368 cases Answer: C Diff: 2 Page Ref: 788 Section Heading: Reorder Point Keywords: economic order quantity model AACSB: Analytical thinking

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121) What is their annual ordering cost if they order at their EOQ level? A) 101.6 B) 203.1 C) 406.2 D) 812.4 Answer: D Diff: 2 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: economic order quantity model AACSB: Analytical thinking

122) What is the increase in their EOQ if all of the model parameters (except the number of days in a year) double? A) 100% B) 33% C) 41% D) 50% Answer: C Diff: 2 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: economic order quantity model AACSB: Analytical thinking

123) Assumptions of the EOQ model include: A) Demand is normally distributed. B) Lead time is normally distributed. C) There is instantaneous order receipt. D) Backorders can occur. Answer: C Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity models AACSB: Application of knowledge

124) In the basic EOQ model, if lead time increases from 5 to 10 days, the EOQ will: A) double. B) increase, but not by double the amount. C) remain the same. D) decrease. Answer: C Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model, econ order quantity models, assumption of EOQ models AACSB: Analytical thinking

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The Krewe of Orpheus The Krewe of Orpheus maintains a supply of swizzle sticks for events throughout the year. Demand for swizzle sticks is shockingly low, a quick check of krewe records from last year reveals that they used only 585,000, but the krewe president believes that they should be good stewards of what they have, so they seek to manage this inventory using the EOQ policy, although they prefer to refer to it as an EOKrewe policy for obvious reasons. Swizzle sticks are not expensive items, they cost a nickel apiece largely due to the club logo printed on each one. This also serves to increase the lead time as they can't be obtained from a standard restaurant supply house. Instead, they must be ordered with an eye towards the six day lead time. It costs $15 to place an order, most of this cost is a result of explaining the meaning of "Laissez les bons temps rouler" and why it should be printed on the edge of each swizzle stick. Holding cost is 20% of purchase price. 125) What should the order quantity for swizzle sticks be? A) 41892 B) 34326 C) 26548 D) 18374 Answer: A Diff: 2 Page Ref: 771 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity AACSB: Analytical thinking

126) What is the average inventory if they order at their EOKrewe quantity? A) 41892 B) 20946 C) 18374 D) 9187 Answer: B Diff: 2 Page Ref: 772 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity AACSB: Analytical thinking

127) What is their total inventory policy cost (excluding cost of goods) if they order at their EOKrewe amount? A) $936.75 B) $468.37 C) $418.93 D) $209.46 Answer: C Diff: 2 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

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128) How many orders will they place in a year if they order optimally (in accordance with the EOQ policy)? A) about 8 B) about 10 C) about 12 D) about 14 Answer: D Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity AACSB: Analytical thinking

129) How much time passes between orders if they order optimally (in accordance with the EOQ policy)? A) 26 days B) 28 days C) 29 days D) 31 days Answer: A Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity AACSB: Analytical thinking

130) After calculating the EOQ and informing their supplier of their order amount, they are informed that the supplier is reluctant to break a case, that is, there are 10,000 swizzle sticks in a case and they must be ordered in multiples of that amount. Not wanting to understock, the krewe decides to round up to the next highest multiple of 10,000. What is their total inventory policy cost (excluding cost of goods) if they order at this amount? A) $936.75 B) $425.50 C) $418.93 D) $209.46 Answer: B Diff: 2 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

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131) After calculating the EOQ and informing their supplier of their order amount, they are informed that the supplier is reluctant to break a case, that is, there are 10,000 swizzle sticks in a case and they must be ordered in multiples of that amount. Not wanting to understock, the krewe decides to round up to the next highest multiple of 10,000. What is the increase in holding cost if they order at this amount? A) $36.75 B) $42.50 C) $40.54 D) $39.46 Answer: C Diff: 2 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

132) After calculating the EOQ and informing their supplier of their order amount, they are informed that the supplier is reluctant to break a case, that is, there are 10,000 swizzle sticks in a case and they must be ordered in multiples of that amount. Not wanting to understock, the krewe decides to round up to the next highest multiple of 10,000. What is the decrease in ordering cost if they order at this amount? A) $36.75 B) $32.50 C) $41.93 D) $33.96 Answer: D Diff: 2 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: EOQ model AACSB: Analytical thinking

133) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. What is the optimal batch size? A) 126,548 B) 99,856 C) 74,268 D) 56,593 Answer: A Diff: 2 Page Ref: 778 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

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134) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. What is the average inventory if they produce an optimal batch size? A) 66224 B) 6934 C) 7256 D) 7528 Answer: B Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

135) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. What is the maximum inventory level if they produce at an optimal batch size? A) 13,268 B) 13,468 C) 13,868 D) 14,268 Answer: C Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

136) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. What is their total cost (including goods) if they produce at an optimal batch size? Note that the price of the swizzle sticks didn't drop, the retired professor just wanted to keep busy. A) $36,751 B) $32,507 C) $31,934 D) $29,389 Answer: D Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

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137) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. How long does it take to produce the optimal batch size? A) 10 weeks B) 9 weeks C) 8 weeks D) 7 weeks Answer: A Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

138) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. How many days per year will the Swizzo 2025 be running if they produce the optimal batch size? A) 340 B) 325 C) 310 D) 295 Answer: B Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

139) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. How many production runs per year will the Swizzo 2025 be producing if they produce the optimal batch size? A) 3.8 B) 4.2 C) 4.6 D) 4.9 Answer: C Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

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140) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. What will be their annual holding cost if they produce the optimal batch size? A) 58.63 B) 62.20 C) 65.77 D) 69.34 Answer: D Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

141) A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. They run through the calculations and realize that with the space taken up by the machine, they can't possibly produce an optimal batch, so they cut the batch size down to a manageable 60,000 units. If a swizzle stick takes up 0.5 cubic inches, how much warehouse space will they save at peak inventory levels compared to producing the optimal batch size? A) 2.11 cubic feet B) 4.31 cubic feet C) 6.57 cubic feet D) 9.34 cubic feet Answer: A Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

142) The economic production quantity is 500 units (units are delivered to the user department as they come off the production line). If the firm decides to buy this item from an outside supplier rather than producing it, the economic purchase quantity would probably be (assume that inventory costs of production and purchasing an item are the same): A) less than 500 units. B) more than 500 units. C) 500 units. D) The direction of change in quantity cannot be determined without additional information. Answer: B Diff: 3 Page Ref: 778 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: economic production quantity model, non-instant receipts model AACSB: Analytical thinking

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143) If order quantity is increased, annual holding cost ________, annual order cost ________, and change in annual total cost ________. A) decreases, increases, is positive B) decreases, increases, cannot be determined C) increases, decreases, is negative D) increases, decreases, cannot be determined Answer: D Diff: 3 Page Ref: 773 Section Heading: The Basic EOQ Model Keywords: economic order quantity model AACSB: Analytical thinking

144) In an EOQ model, as the carrying cost increases, the order quantity: A) increases. B) decreases. C) remains the same. D) cannot be determined. Answer: B Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity AACSB: Analytical thinking

145) In the basic EOQ model, if D = 60 per month, Co = $12, and Cc = $10 per unit per month, what is the EOQ? A) 11 B) 12 C) 13 D) 14 Answer: B Diff: 1 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity models AACSB: Analytical thinking

146) In the basic EOQ model, if annual demand is 50, carrying cost is $2 per unit per year, and ordering cost is $15, what is the EOQ? A) 27.39 B) 26.39 C) 25.39 D) 24.39 Answer: A Diff: 1 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity models AACSB: Analytical thinking

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147) The daily sales of a peanut butter at Power's Grocery are normally distributed, with a mean of 12 jars and a standard deviation of 4. The manager checks the inventories on shelves and places an order every three days. Delivery lead time is two days and they carry 21 jars for safety stock. If there are 4 jars on the shelf when an order is placed, how much should the store order? A) 77 B) 81 C) 32 D) 36 Answer: A Diff: 1 Page Ref: 793 Section Heading: Order Quantity for a Periodic Inventory System Keywords: periodic review AACSB: Analytical thinking

148) In a noninstantaneous receipt model, daily demand is 55 units and daily production is 120 units, C o = $70 and Cc = $4 per unit per year. What is the maximum inventory level? (Assume that the facility is open 365 days per year.) A) 616.9 B) 618.4 C) 620.3 D) 622.9 Answer: A Diff: 2 Page Ref: 778 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: noninstantaneous receipt model AACSB: Analytical thinking

149) A firm is currently purchasing an item for inventory using the basic EOQ model. They plan on making the product themselves and will be using the EOQ model based on noninstantaneous receipt of inventory. If everything else stays the same, what changes should the firm expect? A) EOQ decreases. B) Average inventory level decreases. C) Reorder point increases. D) Safety stock increases. Answer: B Diff: 3 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: noninstantaneous receipt model, economic production model AACSB: Analytical thinking

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150) When using the EOQ Formula with noninstantaneous production, as the demand rate (D) increases up to the rate of production, the EOQ: A) increases. B) decreases. C) remains the same. D) cannot be determined. Answer: A Diff: 3 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: noninstantaneous receipt model, economic production model AACSB: Analytical thinking

151) The diagram above represents which type of inventory model? A) Economic Order Quantity (EOQ) B) EOQ with Noninstantaneous Receipt C) Economic Production Quantity D) Fixed Period Model Answer: B Diff: 1 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: EOQ with noninstantaneous receipt AACSB: Application of knowledge

152) The slope of the line labeled "B" in the diagram is: A) rate of inventory demand. B) production rate. C) shipping rate. D) production rate minus rate of inventory demand. Answer: D Diff: 2 Page Ref: 767 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: EOQ with noninstantaneous receipt AACSB: Analytical thinking

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153) The slope of the line labeled "A" in the diagram is: A) order rate. B) rate of inventory demand. C) production rate. D) production rate minus rate of inventory demand. Answer: C Diff: 3 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: EOQ with noninstantaneous receipt AACSB: Analytical thinking

154) The slope of the line labeled "C" in the diagram is: A) order rate. B) rate of inventory demand. C) production rate. D) shipping rate. Answer: B Diff: 2 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: EOQ with noninstantaneous receipt AACSB: Analytical thinking

155) The interval labeled "E" in the diagram is: A) production cycle. B) production run length. C) shipping lead time. D) inventory fill rate. Answer: A Diff: 3 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: EOQ with noninstantaneous receipt AACSB: Analytical thinking

156) The interval labeled "D" in the diagram is: A) production cycle. B) order receipt period. C) shipping lead time. D) inventory fill rate. Answer: B Diff: 1 Page Ref: 777 Section Heading: The EOQ Model with Noninstantaneous Receipt Keywords: EOQ with noninstantaneous receipt AACSB: Application of knowledge

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157) A product has demand during lead time of 100 units, with a standard deviation of 25 units. What safety stock provides (approximately) a 95% service level? A) 41 B) 55 C) 95 D) 140 Answer: A Diff: 3 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: EOQ model with shortages AACSB: Analytical thinking

158) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year, and Cs = $25, what is the total annual shortage cost? A) 296.51 B) 298.53 C) 299.17 D) 285.91 Answer: A Diff: 3 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages AACSB: Analytical thinking

159) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year, and Cs = $25, what is the order quantity? A) 394.72 B) 495.74 C) 296.51 D) 456.34 Answer: B Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages AACSB: Analytical thinking

160) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year, and Cs = $25, what is the optimal stock out level? A) 96.44 B) 102.36 C) 108.44 D) 114.64 Answer: C Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the optimal stock out level AACSB: Analytical thinking

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161) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year, and Cs = $25, what is the annual carrying cost? A) 1059.03 B) 1355.55 C) 296.51 D) 495.74 Answer: A Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the annual carrying cost AACSB: Analytical thinking

162) Given an EOQ model with shortages in which annual demand is 4200 units, C o = $160, Cc = $7 per unit per year, and Cs = $25, what is the annual ordering cost? A) 2711.09 B) 1059.03 C) 1355.55 D) 495.74 Answer: C Diff: 2 Page Ref: 780 Section Heading: The EOQ Model with Shortages Keywords: EOQ model with shortages, the annual ordering cost AACSB: Analytical thinking

The manager of the Quick Stop Corner convenience store (which is open 360 days per year) sells four cases of Stein soda each day (1440 cases per year). Order costs are $8.00 per order. The lead time for an order is three days. Annual holding costs are equal to $57.60 per case. 163) If the manager orders 16 cases each time she places an order, what is the average inventory level? A) 4 cases B) 8 cases C) 12 cases D) 20 cases Answer: B Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: economic order quantity, EOQ AACSB: Analytical thinking

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164) If the manager orders 16 cases each time she places an order, how many orders would she place in a year? A) 22.5 B) 50 C) 72 D) 90 Answer: D Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: economic order quantity, EOQ AACSB: Analytical thinking

165) What is the optimal order quantity for Stein soda? A) 8 cases B) 12 cases C) 20 cases D) 16 cases Answer: C Diff: 2 Page Ref: 774 Section Heading: The Basic EOQ Model Keywords: economic order quantity, EOQ AACSB: Analytical thinking

166) What is the reorder point for Stein soda? A) 4 cases B) 8 cases C) 12 cases D) 16 cases Answer: C Diff: 2 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

167) If the daily demand is 50 and the lead time in days is 4, what is the reorder point? A) 200 B) 220 C) 240 D) 260 Answer: A Diff: 1 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

37 .

168) If the daily demand is 40 and the level time in days is 4, what is the reorder point? A) 120 B) 140 C) 160 D) 180 Answer: C Diff: 1 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

169) If the daily demand is 10 and the lead time in days is 8, what is the reorder point? A) 60 B) 70 C) 80 D) 90 Answer: C Diff: 1 Page Ref: 788 Section Heading: Reorder Point Keywords: reorder point AACSB: Analytical thinking

170) If average demand for an inventory item is 200 units per day, lead time is 3 days, and safety stock is 100 units, what is the reorder point? A) 500 B) 600 C) 700 D) 800 Answer: C Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: reorder point AACSB: Analytical thinking

171) Ruby owns a small cafe and uses a linen supplier for her tablecloths. Whenever she needs more tablecloths, she calls the supplier. She uses an average of 12 tablecloths a day with a standard deviation of 3 tablecloths. Lead time is a constant 2 days. If Ruby is willing to accept a 5% stockout risk, what is the reorder point, rounded to the nearest tablecloth? Assume demand is normally distributed. A) 28 B) 31 C) 34 D) 42 Answer: B Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: reorder point AACSB: Analytical thinking

38 .

172) The service level is the probability that: A) the inventory will meet demand. B) the inventory available during lead time will meet demand. C) the inventory available during lead time will not meet demand. D) the inventory will not meet demand. Answer: B Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: safety stocks, service levels AACSB: Application of knowledge

173) What service level results in zero safety stock in reorder point calculations? A) 0% B) 33% C) 50% D) 80% Answer: C Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: safety stock, service level AACSB: Analytical thinking

174) The ________ is the probability that the inventory available during lead time will meet demand. A) service level B) inventory level C) reorder point D) maximum inventory level Answer: A Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: safety stocks, service levels AACSB: Application of knowledge

175) If annual demand equals 1000 units, the number of working days per year is 250, C o = $300 per order and Cc = $3 per unit, how many days are between orders in the basic EOQ model? A) 110 B) 112 C) 117 D) 122 Answer: B Diff: 2 Page Ref: 775 Section Heading: The Basic EOQ Model Keywords: EOQ model, economic order quantity models AACSB: Analytical thinking

39 .

176) As service level increases, expected number of stockouts ________ and safety stock ________. A) increase, increases B) decrease, decreases C) decrease, increases D) increase, decreases Answer: C Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: safety stock, service level AACSB: Analytical thinking

177) Adding 1.5 standard deviations of safety stock to the average demand during lead time will result in a service level of approximately: A) 68.4%. B) 84.1%. C) 93.3%. D) 97.7%. Answer: C Diff: 2 Page Ref: 790 Section Heading: Determining Safety Stocks Using Service Levels Keywords: safety stock, service level AACSB: Analytical thinking

178) A periodic inventory system: A) uses fixed order sizes at variable time intervals. B) normally requires a larger safety stock. C) cannot be used if demand is variable. D) is used to periodically manage inventory. Answer: B Diff: 2 Page Ref: 793 Section Heading: Order Quantity for a Periodic Inventory System Keywords: periodic inventory system, fixed time period inventory system AACSB: Application of knowledge

40 .

Introduction to Management Science, 12e (Taylor) Module A: The Simplex Solution Method 1) The simplex method cannot be used to solve quadratic programming problems. Answer: TRUE Diff: 3 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

2) The simplex method is a general mathematical solution technique for solving linear programming problems. Answer: TRUE Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

3) In the simplex method, the model is put into the form of a table, and then a number of mathematical steps are performed on the table. Answer: TRUE Diff: 3 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

4) The simplex method can be used to solve quadratic programming problems. Answer: FALSE Diff: 3 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

5) The simplex method is a general mathematical solution technique for solving nonlinear programming problems. Answer: FALSE Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

6) The simplex method moves from one better solution to another until the best one is found, and then it stops. Answer: TRUE Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

1 .

7) The mathematical steps in the simplex method replicate the process in graphical analysis of moving from one extreme point on the solution boundary to another. Answer: TRUE Diff: 1 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

8) The first step in solving a linear programming model manually with the simplex method is to convert the model into standard form. Answer: TRUE Diff: 1 Section Heading: Converting the Model into Standard Form Keywords: standard form, simplex method AACSB: Application of knowledge

9) The last step in solving a linear programming model manually with the simplex method is to convert the model into standard form. Answer: FALSE Diff: 1 Section Heading: Converting the Model into Standard Form Keywords: standard form, simplex method AACSB: Application of knowledge

10) Slack variables are added to constraints and represent unused resources. Answer: TRUE Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: slack variables, simplex method AACSB: Application of knowledge

11) Artificial variables are added to constraints and represent unused resources. Answer: FALSE Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: artificial variables, slack variables, simplex method AACSB: Application of knowledge

12) A basic feasible solution satisfies the model constraints and has the same number of variables with non-negative values as there are constraints. Answer: TRUE Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: basic feasible solution AACSB: Application of knowledge

2 .

13) A basic feasible solution satisfies the model constraints and has the same number of variables with negative values as there are constraints. Answer: FALSE Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: basic feasible solution AACSB: Application of knowledge

14) Row operations are used to solve simultaneous equations where equations are multiplied by constants and added or subtracted from each other. Answer: TRUE Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: simultaneous equations, row operations AACSB: Application of knowledge

15) The basic feasible solution in the initial simplex tableau is the origin where all decision variables equal zero. Answer: TRUE Diff: 1 Section Heading: The Simplex Method Keywords: basic feasible solution, initial simplex tableau AACSB: Application of knowledge

16) At the initial basic feasible solution at the origin, only slack variables have a value greater than zero. Answer: TRUE Diff: 2 Section Heading: The Simplex Method Keywords: basic/initial basic feasible solution, slack variables AACSB: Application of knowledge

17) At the initial basic feasible solution at the origin, only slack variables have a value greater than 1. Answer: FALSE Diff: 2 Section Heading: The Simplex Method Keywords: basic/initial basic feasible solution, slack variables AACSB: Application of knowledge

18) In using the simplex method, the number of basic variables is equal to the number of constraints. Answer: TRUE Diff: 2 Section Heading: The Simplex Method Keywords: basic feasible solution, constraints AACSB: Application of knowledge

19) The simplex method does not guarantee an integer solution. Answer: TRUE Diff: 1 Section Heading: The Simplex Method Keywords: simplex method AACSB: Application of knowledge

3 .

20) In solving a linear programming problem with simplex method, the number of basic variables is the same as the number of constraints in the original problem. Answer: TRUE Diff: 2 Section Heading: The Simplex Method Keywords: simplex method AACSB: Application of knowledge

21) A change in the objective function coefficient of a basic variable cannot change the value of z j for a non-basic variable in the final simplex tableau. Answer: FALSE Diff: 3 Section Heading: The Simplex Method Keywords: simplex method AACSB: Application of knowledge

22) When solving a linear programming problem, a decision variable that leaves the basis in one iteration of the simplex method can return to the basis on a later iteration. Answer: TRUE Diff: 3 Section Heading: The Simplex Method Keywords: simplex method AACSB: Application of knowledge

23) Final tableaus cannot be used to conduct sensitivity analysis. Answer: FALSE Diff: 1 Section Heading: The Simplex Method Keywords: simplex method AACSB: Application of knowledge

24) The dual form of a linear program is used to determine how much one should pay for additional resources. Answer: TRUE Diff: 1 Section Heading: The Simplex Method Keywords: dual AACSB: Application of knowledge

25) Multiple optimal solutions cannot be determined from the simplex method. Answer: FALSE Diff: 1 Section Heading: The Simplex Method Keywords: simplex method AACSB: Application of knowledge

4 .

26) The theoretical limit on the number of decision variables that can be handled by the simplex method is 50. Answer: FALSE Diff: 1 Section Heading: The Simplex Method Keywords: simplex method AACSB: Application of knowledge

27) The ________ column is the column corresponding to the entering variable. Answer: pivot Diff: 2 Section Heading: The Simplex Method Keywords: pivot column AACSB: Application of knowledge

28) The variable with the largest positive cj - zj is the ________ variable. Answer: entering Diff: 2 Section Heading: The Simplex Method Keywords: entering variable AACSB: Application of knowledge

29) ________ variables are added to constraints and represent unused resources. Answer: Slack Diff: 2 Section Heading: Simplex Solution of a Minimization Problem Keywords: slack variables AACSB: Application of knowledge

30) The first step in solving a linear programming model manually with the simplex method is to convert the model into ________ form. Answer: standard Diff: 2 Section Heading: Summary of the Simplex Method Keywords: standard form AACSB: Application of knowledge

31) The ________ values are contribution to profit for each variable. Answer: cj Diff: 2 Section Heading: The Simplex Method Keywords: cj values, contribution to profit. AACSB: Application of knowledge

5 .

32) The ________ values are computed by multiplying the c j column values by the variable column values and summing. Answer: zj Diff: 2 Section Heading: The Simplex Method Keywords: zj values AACSB: Application of knowledge

33) The ________ variable allows for an initial basic feasible solution, but it has no meaning. Therefore, after we get the simplex tableau started, they are discarded in later iterations. Answer: artificial Diff: 2 Section Heading: Irregular Types of Linear Programming Problems Keywords: artificial variables AACSB: Application of knowledge

34) In solving a minimization problem, artificial variables are assigned a ________ in the objective function to eliminate them from the final solution. Answer: large cost Diff: 2 Section Heading: Simplex Solution of a Minimization Problem Keywords: artificial variables AACSB: Application of knowledge

35) A(n) ________ maximization linear programming problem has an artificial variable in the final simplex tableau where all cj - zj values are less than or equal to zero. Answer: infeasible Diff: 2 Section Heading: Irregular Types of Linear Programming Problems Keywords: infeasible problem, infeasible solution AACSB: Application of knowledge

36) In using the simplex method, ________ optimal solutions are identified by c j - zj = 0 for a non-basic variable. Answer: multiple or alternative Diff: 2 Section Heading: Irregular Types of Linear Programming Problems Keywords: alternative optimal solutions, multiple optimal solutions AACSB: Application of knowledge

37) A primal maximization model with ≤ constraints converts to a ________ minimization model with constraints. Answer: dual Diff: 2 Section Heading: The Dual Keywords: dual model AACSB: Application of knowledge

6 .

38) The quantity values on the right-hand side of the primal inequality constraints are the ________ coefficients in the dual. Answer: objective function Diff: 2 Section Heading: The Dual Keywords: dual model AACSB: Application of knowledge

39) If the primal problem has three constraints, then the corresponding dual problem will have three ________. Answer: decision variables Diff: 2 Section Heading: The Dual Keywords: dual model AACSB: Application of knowledge

40) Whereas the maximization primal model has ≤ constraints, the ________ dual model has ≥ constraints. Answer: minimization Diff: 1 Section Heading: The Dual Keywords: dual model AACSB: Application of knowledge

41) ________ in linear programming is when a basic variable takes on a value of zero (i.e., a zero in the right-hand side of the constraints of the tableau). Answer: Degeneracy Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: degeneracy AACSB: Application of knowledge

42) In a ________ problem, artificial variables are assigned a very high cost. Answer: minimization Diff: 1 Section Heading: Simplex Solution of a Minimization Problem Keywords: artificial variables AACSB: Application of knowledge

43) A(n) ________ problem can be identified in the simplex procedure when it is not possible to select a pivot row. Answer: unbounded Diff: 2 Section Heading: Irregular Types of Linear Programming Problems Keywords: simplex irregularity, unbounded solution AACSB: Application of knowledge

7 .

44) The ________ form of a linear program is used to determine how much one should pay for additional resources. Answer: dual Diff: 2 Section Heading: The Dual Keywords: dual AACSB: Application of knowledge

45) To determine the sensitivity range for the coefficient of a variable in the objective function, calculations are performed such that all values in the cj - zj row are ________. Answer: less than or equal to zero Diff: 2 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Application of knowledge

46) Given the following linear programming problem: maximize 4x1 + 3x2 subject to

4x1 + 3x2 ≤ 23 5x1 - x2 ≤ 5 x1, x2 ≥ 0

What are the basic variables in the initial tableau? Answer: S1, S2 Diff: 1 Section Heading: The Simplex Method Keywords: basic variables, initial tableau AACSB: Analytical thinking

47) Given the following linear programming problem: maximize 4x1 + 3x2 subject to

4x1 + 3x2 ≤ 23 5x1 - x2 ≤ 5 x1, x2 ≥ 0

What are the Cj values for the basic variables? Answer: 0, 0 Diff: 1 Section Heading: The Simplex Method Keywords: basic variables, objective function coefficients AACSB: Analytical thinking

8 .

48) Given the following linear programming problem: maximize 4x1 + 3x2 subject to

4x1 + 3x2 ≤ 23 5x1 - x2 ≤ 5 x1, x2 ≥ 0

What is the (Cj - Zj) value for S1 at the initial solution? Answer: 0 Diff: 1 Section Heading: The Simplex Method Keywords: Cj - Zj values AACSB: Analytical thinking

49) Given the following linear programming problem: maximize 4x1 + 3x2 subject to

4x1 + 3x2 ≤ 23 5x1 - x2 ≤ 5 x1, x2 ≥ 0

What is the (Ci- Zi) value for S2 at the initial solution? Answer: 0 Diff: 1 Section Heading: The Simplex Method Keywords: Cj - Zj values AACSB: Analytical thinking

50) Given the following linear programming problem: maximize 4x1 + 3x2 subject to

4x1 + 3x2 ≤ 23 5x1 - x2 ≤ 5 x1, x2 ≥ 0

What is the value of X1 in the final tableau? Answer: 0 or 4.25 Diff: 2 Section Heading: The Simplex Method Keywords: simplex method, simplex tableaus AACSB: Analytical thinking

51) Given the following linear programming problem: maximize 4x1 + 3x2 subject to

4x1 + 3x2 ≤ 23 5x1 - x2 ≤ 5 x1, x2 ≥ 0

What is the value of x2 in the final tableau? Answer: 2 or 7.667 Diff: 2 Section Heading: The Simplex Method Keywords: simplex method, simplex tableaus AACSB: Analytical thinking

9 .

52) Solve the following problem using the simplex method. Minimize

Z = 3x1 + 4x2 + 8x3

Subject to: 2x1 + x2 ≥ 6 x2 + 2x3 ≥ 4 x1, x2 ≥ 0 Answer: x1 = 1, x2 = 4, x3 = 0 and Z = 19 Diff: 3 Section Heading: The Simplex Method Keywords: simplex method, simplex tableaus AACSB: Analytical thinking

53) Solve the following problem using the simplex method. Minimize

Z = 2x1 + 6x2

Subject to: 2x1 + 4x2 ≤ 12 3x1 + 2x2 ≥ 9 x1, x2 ≥ 0 Answer: x1 = 1.5, x2 = 2.25, and Z = 16.5 Diff: 3 Section Heading: The Simplex Method Keywords: simplex method, simplex tableaus AACSB: Analytical thinking

54) Given the following linear programming problem: maximize

4x1 + 3x2

subject to

4x1 + 3x2 ≤ 23 5x1 - x2 ≤ 5 x1, x2 ≥ 0

What is the optimal value of this objective function? Answer: 23 Diff: 2 Section Heading: The Simplex Method Keywords: objective function value, simplex tableaus AACSB: Analytical thinking

10 .

55) Given the following linear programming problem: maximize

4x1 + 3x2

subject to

4x1 + 3x2 ≤ 23 5x1 - x2 ≤ 5 x1, x2 ≥ 0

How many iterations did we have to perform before reaching the final tableau? Answer: 3 Diff: 3 Section Heading: The Simplex Method Keywords: simplex tableaus, simplex iterations AACSB: Analytical thinking

56) Given the following linear programming problem: maximize

Z = $100x1 + 80x2

subject to

x1 + 2x2 ≤ 40 3x1 + x2 ≤ 60 x1, x2 ≥ 0

Using the simplex method, what is the optimal value for X1? Answer: 16 Diff: 2 Section Heading: The Simplex Method Keywords: simplex tableaus, simplex iterations AACSB: Analytical thinking

57) Given the following linear programming problem: maximize

Z = $100x1 + 80x2

subject to

x1 + 2x2 ≤ 40 3x1 + x2 ≤ 60 x1, x2 ≥ 0

Using the simplex method, what is the optimal value for X2? Answer: 12 Diff: 2 Section Heading: The Simplex Method Keywords: simplex tableaus, simplex iterations AACSB: Analytical thinking

11 .

58) Given the following linear programming problem: maximize

Z = $100x1 + 80x2

subject to

x1 + 2x2 ≤ 40 3x1 + x2 ≤ 60 x1, x2 ≥ 0

Using the simplex method, what is the value for S2 in the optimal tableau? Answer: 0 Diff: 2 Section Heading: The Simplex Method Keywords: simplex tableaus, simplex iterations AACSB: Analytical thinking

59) Given the following linear programming problem: maximize Z = $100x1 + 80x2 subject to

x1 + 2x2 ≤ 40 3x1 + x2 ≤ 60 x1, x2 ≥ 0

Using the simplex method, what is the optimal value for the objective function? Answer: $2560 Diff: 2 Section Heading: The Simplex Method Keywords: objective function value AACSB: Analytical thinking

60) Given the following linear programming problem: maximize

Z = $100x1 + 80x2

subject to

x1 + 2x2 ≤ 40 3x1 + x2 ≤ 60 x1, x2 ≥ 0

Using the simplex method, what is the value for S1 in the final basic feasible solution? Answer: 0 Diff: 2 Section Heading: The Simplex Method Keywords: slack variables, simplex iterations AACSB: Analytical thinking

12 .

The linear programming problem whose output follows determines how many red nail polishes, blue nail polishes, green nail polishes, and pink nail polishes a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions. MAX

100x1 + 120x2 + 150x3 + 125x4

Subject to 1. x1 + 2x2 + 2x3 + 2x4 ≤ 108 2. 3x1 + 5x2 + x4 ≤ 120 3. x1 + x3 ≤ 25 4. x2 + x3 + x4 > 50 x1, x2, x3, x4 ≤ 0 Optimal Solution: Objective Function Value = 7475.000

Objective Coefficient Ranges

Right Hand Side Ranges

61) How much space will be left unused? Answer: 0 Diff: 1 Section Heading: The Simplex Method Keywords: computer output of linear programming method, slack variables AACSB: Analytical thinking

13 .

62) How much time will be used? Answer: 57 Diff: 2 Section Heading: The Simplex Method Keywords: computer output of linear programming problems, slack variables AACSB: Analytical thinking

63) By how much will the second marketing restriction be exceeded? Answer: 0 Diff: 2 Section Heading: The Simplex Method Keywords: computer output of linear programming problems, slack variables AACSB: Analytical thinking

64) What is the profit? Answer: 7475 Diff: 2 Section Heading: The Simplex Method Keywords: comp output of linear prog problems, objective function value AACSB: Analytical thinking

65) To what value can the profit on red nail polish drop before the solution would change? Answer: 87.5 Diff: 2 Section Heading: The Simplex Method Keywords: computer output of linear prog problems, sensitivity analysis AACSB: Analytical thinking

66) By how much can the profit on green nail polish increase before the solution would change? Answer: 12.5 Diff: 2 Section Heading: The Simplex Method Keywords: computer output of linear prog problems, sensitivity analysis AACSB: Analytical thinking

67) By how much can the amount of space decrease before there is a change in the profit? Answer: 0 Diff: 2 Section Heading: The Simplex Method Keywords: computer output of linear prog problems, sensitivity analysis AACSB: Analytical thinking

68) You are offered the chance to obtain more space. The offer is for 15 units and the total price is 1500. What should you do? Answer: Reject the offer. Diff: 2 Section Heading: The Simplex Method Keywords: computer output of linear prog problems, sensitivity analysis AACSB: Analytical thinking

14 .

69) Consider the following linear programming problem: MAX

Z = 10

+ 30

s.t.

≤ 12

≤ 16

Use the two tables below to create the initial tableau and perform 1 pivot.

15 .

Answer:

Diff: 2 Section Heading: The Simplex Method Keywords: simplex procedure AACSB: Analytical thinking

16 .

70) Consider the following linear programming problem and the corresponding final tableau. MAX

Z=3

s.t.

≤4 2

≤ 12

≥ 18

What is the shadow price for each constraint? Answer: constraint 1, 3; constraint 2, 2.5; constraint 3, 0 Diff: 2 Section Heading: The Simplex Method Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking

17 .

71) Consider the following linear programming problem and the corresponding final tableau. MAX

Z=3

s.t.

≤4 2

≤ 12

≥ 18

What is the sensitivity range for the first constraint? Answer: maximum decrease of 2, and an infinite increase Diff: 2 Section Heading: The Simplex Method Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking

72) Write the dual form of the following linear program. MAX

Z=3

s.t.

≤4 2

≤ 12

≥ 18

Answer: MIN

+ 12

s.t.

≥3

≥5

+ 18

Diff: 2 Section Heading: The Simplex Method Keywords: dual form AACSB: Analytical thinking

18 .

73) The simplex method ________ be used to solve quadratic programming problems. A) can B) cannot C) may D) should Answer: B Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

74) The simplex method is a general mathematical solution technique for solving ________ programming problems. A) integer B) non-linear C) linear D) A, B, and C Answer: C Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: simplex method AACSB: Application of knowledge

75) Slack variables are added to ________ constraints and represent unused resources. A) ≤ B) < C) ≥ D) > E) = Answer: A Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: slack variables AACSB: Application of knowledge

76) The ________ step in solving a linear programming model manually with the simplex method is to convert the model into standard form. A) first B) second C) last D) only Answer: A Diff: 2 Section Heading: Converting the Model into Standard Form Keywords: standard form, simplex method AACSB: Application of knowledge

19 .

77) Row operations are used to solve simultaneous equations where equations are ________ by constants and added to or subtracted from each other. A) converted B) restrained C) divided D) multiplied Answer: D Diff: 3 Section Heading: Converting the Model into Standard Form Keywords: row operations, simultaneous equations AACSB: Application of knowledge

78) The basic feasible solution in the initial simplex tableau is the origin where all decision variables equal: A) 0. B) 1. C) -1. D) 1 or -1. Answer: A Diff: 3 Section Heading: The Simplex Method Keywords: basic feasible solution, initial simplex tableau AACSB: Application of knowledge

79) At the initial basic feasible solution at the origin, only slack variables have a value greater than: A) 0. B) 1. C) -1. D) 1 or -1. Answer: A Diff: 3 Section Heading: The Simplex Method Keywords: basic feasible solution, initial simplex tableau AACSB: Application of knowledge

80) At the initial basic feasible solution at the origin, only ________ variables have a value greater than zero. A) linear B) slack C) non-linear D) integer Answer: B Diff: 1 Section Heading: The Simplex Method Keywords: basic feasible solution AACSB: Application of knowledge

20 .

81) The leaving variable is determined by ________ the quantity values ________ the pivot column values and selecting the minimum possible value or zero. A) adding, to B) multiplying, by C) dividing, by D) subtracting, from Answer: C Diff: 2 Section Heading: The Simplex Method Keywords: simplex tableau, leaving variable AACSB: Application of knowledge

82) The leaving variable is determined by dividing the quantity values by the pivot column values and selecting the: A) maximum positive value. B) minimum negative value. C) minimum positive value. D) maximum negative value. Answer: C Diff: 3 Section Heading: The Simplex Method Keywords: simplex tableau, leaving variable AACSB: Application of knowledge

83) The simplex method ________ guarantee integer solutions. A) sometimes does B) does C) does not D) may Answer: C Diff: 2 Section Heading: The Simplex Method Keywords: simplex method AACSB: Application of knowledge

84) For a maximization linear programming problem, a(n) ________ is ________ for a less-than-or-equalto constraint. A) surplus, subtracted B) slack, added C) artificial, added D) artificial, subtracted E) surplus, added Answer: B Diff: 2 Section Heading: The Simplex Method Keywords: slack variables AACSB: Application of knowledge

21 .

85) The objective function coefficient of an artificial variable for a minimization linear programming problem is: A) +M. B) -M. C) 0. D) 1. E) an arbitrary value between 0 and positive infinity Answer: A Diff: 2 Section Heading: The Simplex Method Keywords: artificial variables AACSB: Application of knowledge

86) If a slack variable has a positive value (is basic) in the optimal solution to a linear programming problem, then the shadow price of the associated constraint: A) is always zero. B) is always greater than zero. C) is always less than zero. D) could be any value (i.e., zero greater than zero or less than zero). Answer: A Diff: 2 Section Heading: The Simplex Method Keywords: slack variable, shadow price AACSB: Application of knowledge

87) In the simplex procedure, if cj - zj = 0 for a non-basic variable, this indicates that: A) the solution is infeasible. B) the solution is unbounded. C) there are multiple optimal solutions. D) the formulation is incorrect. Answer: C Diff: 2 Section Heading: The Simplex Method Keywords: simplex irregularity, multiple optimal solutions AACSB: Application of knowledge

88) In the simplex procedure, if it is not possible to select a pivot row, this indicates that: A) the solution is infeasible. B) the solution is unbounded. C) there are multiple optimal solutions. D) the formulation is incorrect. Answer: B Diff: 2 Section Heading: The Simplex Method Keywords: simplex irregularity, unbounded solution AACSB: Application of knowledge

22 .

89) In the simplex procedure, if all cj - zj ≤ 0 and one or more of the basic variables are artificial, this indicates that: A) the solution is infeasible. B) the solution is unbounded. C) there are multiple optimal solutions. D) the formulation is incorrect. Answer: A Diff: 2 Section Heading: The Simplex Method Keywords: simplex irregularity, infeasible solution AACSB: Application of knowledge

90) The ________ form of a linear program is used to determine how much one should pay for additional resources. A) standard B) primal C) feasible D) dual E) simplex Answer: D Diff: 2 Section Heading: The Simplex Method Keywords: dual AACSB: Application of knowledge

23 .

Introduction to Management Science, 12e (Taylor) Module B: Transportation and Assignment Solution Methods 1) In a transportation problem, items are allocated from sources to destinations at a minimum cost. Answer: TRUE Diff: 1 Section Heading: Solution of the Transportation Model Keywords: transportation problem AACSB: Application of knowledge

2) The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination. Answer: TRUE Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation prob, linear prog model for a transportation prob AACSB: Application of knowledge

3) Transportation problems are solved manually within a tableau format. Answer: TRUE Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem AACSB: Application of knowledge

4) In a balanced transportation model where supply equals demand, all constraints are equalities. Answer: TRUE Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem, balanced transportation model AACSB: Application of knowledge

5) In a balanced transportation model where supply equals demand, all constraints are inequalities. Answer: FALSE Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation prob, balanced transportation model, constraints AACSB: Application of knowledge

6) The supply and demand values along the outside rim of a tableau are called rim requirements. Answer: TRUE Diff: 3 Section Heading: Solution of the Transportation Model Keywords: supply and demand values, rim requirements AACSB: Application of knowledge

1 .

7) Unacceptable (prohibited) routes in a transportation problem are assigned cost values of zero. Answer: FALSE Diff: 1 Section Heading: Solution of the Transportation Model Keywords: prohibited routes AACSB: Application of knowledge

8) An assignment problem is a special form of transportation problem where all supply and demand values equal 1. Answer: TRUE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge

9) An assignment problem is a special form of transportation problem where all supply and demand values equal 0. Answer: FALSE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge

10) An opportunity cost table is developed by first subtracting the minimum value in each row from all other row values and then repeating this process for each column. Answer: TRUE Diff: 3 Section Heading: Solution of the Assignment Model Keywords: opportunity cost table AACSB: Application of knowledge

11) An opportunity cost table is developed by first subtracting the minimum value in each row from all other row values and then repeating this process for each row. Answer: FALSE Diff: 3 Section Heading: Solution of the Assignment Model Keywords: opportunity cost table AACSB: Application of knowledge

12) Assignments are made to locations with 0 in the opportunity cost table. Answer: TRUE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge

2 .

13) Assignments are made to locations with 1 in the opportunity cost table. Answer: FALSE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge

14) An optimal solution occurs when the number of independent unique assignments equals the number of rows or columns. Answer: TRUE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: assignment problem, unique assignments AACSB: Application of knowledge

15) If the number of unique assignments is less than the number of rows or columns, a line test must be used. Answer: TRUE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: assignment problem, unique assignments AACSB: Application of knowledge

16) An assignment problem that involves 6 machines to be assigned to 4 workers cannot be solved using the assignment problem solution procedure described. Answer: FALSE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge

17) The transportation model is a special type of linear regression model. Answer: FALSE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: transportation model AACSB: Application of knowledge

18) The transportation model assumes that shipping costs are the same, regardless of the number of units shipped. Answer: TRUE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: transportation model AACSB: Application of knowledge

3 .

19) It is not possible to solve a transportation problem that has ≤ instead of = signs for the supply constraints. Answer: FALSE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: transportation model AACSB: Application of knowledge

20) Transportation problems can be solved by the simplex method. Answer: TRUE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: transportation model AACSB: Application of knowledge

21) When the number of people and the number of tasks are not equal in an assignment problem then the problem cannot be solved. Answer: FALSE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: assignment method AACSB: Application of knowledge

22) In the ________ method, the largest possible allocation is made to the cell in the upper-left-hand corner of the tableau, followed by allocations to adjacent feasible cells. Answer: northwest corner Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method AACSB: Application of knowledge

23) In using the minimum cell cost method, as much as possible is allocated to the cell with the ________ cost. Answer: minimum Diff: 1 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Application of knowledge

24) ________ model is a method for determining an initial solution for a transportation problem based on the concept of penalty cost or regret. Answer: Vogel's approximation Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Application of knowledge

4 .

25) In using the Vogel's Approximation model, a ________ is the difference between the largest and next largest cell cost in a row. Answer: penalty cost Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method, penalty cost AACSB: Application of knowledge

26) Vogel's approximation method allocates to the minimum cost cell in the row or column with the ________ penalty cost. Answer: largest Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method, penalty cost AACSB: Application of knowledge

27) A multiple optimal solution occurs when an empty cell has a cost change of ________ and all other empty cells are positive. Answer: zero Diff: 2 Section Heading: Solution of the Transportation Model Keywords: stepping stone method, MODI AACSB: Application of knowledge

28) When demand exceeds supply, a dummy ________ is added to the solution tableau. Answer: row or supply Diff: 1 Section Heading: The Unbalanced Transportation Problem Keywords: unbalanced transportation problem AACSB: Application of knowledge

29) When supply exceeds demand, a dummy ________ is added to the solution tableau. Answer: column or destination Diff: 1 Section Heading: The Unbalanced Transportation Problem Keywords: unbalanced transportation problem AACSB: Application of knowledge

30) In a transportation tableau with m rows and n columns, if there are fewer than n+m-1 allocations, the tableau is said to be ________. Answer: degenerate Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: transportation tableau, degenerate solution AACSB: Application of knowledge

5 .

31) In a transportation tableau to rectify a degenerate tableau, an empty cell must artificially be treated as an ________ cell. Answer: occupied or full Diff: 3 Section Heading: The Unbalanced Transportation Problem Keywords: degenerate solution, transportation tableau AACSB: Application of knowledge

32) A(n) ________ problem is a special form of transportation problem where all supply and demand values equal 1. Answer: assignment Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: assignment problem AACSB: Application of knowledge

33) A(n) ________ table is developed by first subtracting the minimum value in each row from all other row values and then repeating the process for each column. Answer: opportunity cost Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: opportunity cost table AACSB: Application of knowledge

34) A(n) ________ solution occurs when the number of independent unique assignments equals the number of rows or columns. Answer: optimal Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: optimal solution of the assignment problem, optimal assignments AACSB: Application of knowledge

35) The two solution methods for transportation problems that do not require the use of a computer are ________ and ________. Answer: stepping stone, MODI Diff: 1 Section Heading: The Unbalanced Transportation Problem Keywords: transportation problem solution methods AACSB: Application of knowledge

36) Generally, ________ problems match people to an equal number of tasks at a minimum cost. Answer: assignment Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: assignment AACSB: Application of knowledge

6 .

37) If the number of unique assignments is less than the number of rows, then a ________ test must be used. Answer: line Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: assignment AACSB: Application of knowledge

38) The three methods for identifying initial feasible solutions to transportation problems are ________, ________, and ________. Answer: northwest corner method, minimum cell cost method, Vogel's approximation method Diff: 1 Section Heading: The Unbalanced Transportation Problem Keywords: initial feasible solutions AACSB: Application of knowledge

Given the following transportation tableau—where the numbers in each cell represent transportation costs from the specific source to the specific destination—with supply figures corresponding to each source and demand figures corresponding to each destination:

39) According to the Northwest Corner method, the initial solution would give to cell B2 a loading of ________. Answer: 150 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method AACSB: Analytical thinking

40) According to the Northwest Corner method, the initial solution would have a total transportation cost of ________. Answer: $2600 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method, total cost calculations AACSB: Analytical thinking

41) According to the Vogel's Approximation Method, the initial solution would give to cell B2 a loading of ________. Answer: 100 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Analytical thinking

7 .

42) According to the Vogel's Approximation Method, the initial solution would have a total transportation cost of ________. Answer: $2455 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Analytical thinking

43) According to the minimum cell cost method, the initial solution would give to cell C1 a loading of ________. Answer: 350 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Analytical thinking

44) According to the minimum cell cost method, the initial solution would have a total transportation cost of ________. Answer: $2455 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Analytical thinking

Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below:

Shipping costs are (in $): 45) According to the Northwest Corner method, the initial solution would give to cell CIII a loading of ________. Answer: 125 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method AACSB: Analytical thinking

8 .

46) According to the Northwest Corner method, the initial solution would have a total transportation cost of ________. Answer: $1800 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method AACSB: Analytical thinking

47) According to the Vogel's Approximation Method, the initial solution would give to cell CII a loading of ________. Answer: 0 or 25 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Analytical thinking

48) According to the Vogel's Approximation Method, the initial solution would have a total transportation cost of ________. Answer: $1700 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Analytical thinking

49) According to the minimum cell cost method, the initial solution would give to cell BI a loading of ________. Answer: 25 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Analytical thinking

50) According to the minimum cell cost method, the initial solution would have a total transportation cost of ________. Answer: $1700 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Analytical thinking

9 .

51) 1 2 3 4 DD

SS 100 200 150 50

1 5 4 3 9 250

2 6 2 6 7 250

What is the objective function? Answer: Min 5x11 + 6x12 + 4x21 + 2x22 + 3x31 + 6x32 + 9x41 + 7x42 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, objective function AACSB: Analytical thinking

52) 1 2 3 4 DD

SS 100 200 150 50

1 5 4 3 9 250

2 6 2 6 7 250

What are the supply-side constraints? Answer: x11 +x12 ≤ 100 x21 + x22 ≤ 200 x31 + x32 ≤ 150 x41 + x42 ≤ 50 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, supply-side constraints AACSB: Analytical thinking

53) 1 2 3 4 DD

SS 100 200 150 50

1 5 4 3 9 250

2 6 2 6 7 250

What are the demand-side constraints? Answer: x11 + x21 + x31 + x41 = 250 x12 + x22 + x32 + x42 = 250 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, demand-side constraints AACSB: Analytical thinking

10 .

54) Consider the following transportation tableau with the initial solution provided. Use the stepping stone method to identify a better allocation.

Answer:

Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation, stepping stone AACSB: Analytical thinking

55) An independent operator is planning shipments of gasoline from two sources to three destinations. Per ton transportation costs are given in the following table.

There are 1000 tons available at A and 1300 tons available at B. Since the destinations want as much as possible, the owner has decided to ship out all available quantities. Solve using either stepping stone or MODI. Answer: 1300 tons will be sent to D and 1000 will be sent to C. None will be sent to E, since minimum demand requirements are not specified for each destination. Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem AACSB: Analytical thinking

11 .

56) A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work; however, their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does which manuscript. Estimates of editing times (in hours) for each manuscript by each editor are:

How many variables are involved in this assignment method? Answer: 25 Diff: 3 Section Heading: Solution of the Assignment Model Keywords: assignment model formulation AACSB: Analytical thinking

57) A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work; however, their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does which manuscript. Estimates of editing times (in hours) for each manuscript by each editor are:

How many constraints are needed? Answer: 10 Diff: 3 Section Heading: Solution of the Assignment Model Keywords: assignment model formulation, constraints AACSB: Analytical thinking

12 .

58) The student internship director needs as much coverage as possible in the office next week. The more hours that can be put in each day, the better. She has asked the students to provide a list of how many hours they are available each day of the week. Each student can be there on only one day and there must be a student in the office each day of the week. Use the table below and the tables provided to determine the schedule that gives the most coverage. Note that the objective of this problem is to maximize the hours worked, not minimize. Student A B C D E

Mon 2 3 6 7 4

Tue 4 2 8 4 5

Wed 8 7 6 3 3

Thurs 4 3 5 6 1

Fri 6 2 4 8 4

Answer: 1. Convert to a minimization problem by subtracting each value from 8: Student Mon Tue Wed Thurs Fri A 6 4 0 4 2 B 5 6 1 5 6 C 2 0 2 3 4 D 1 4 5 2 0 E 4 3 5 7 4 2. Subtract the minimum value in each row from all other row values: Student Mon Tue Wed Thurs Fri A 6 4 0 4 2 B 4 5 0 4 5 C 2 0 2 3 4 D 1 4 5 2 0 E 1 0 2 4 1

13 .

3. Subtract the minimum column value in each column from all other column values: Student Mon Tue Wed Thurs Fri A 5 4 0 2 2 B 3 5 0 2 5 C 1 0 2 1 4 D 0 4 5 0 0 E 0 0 2 2 1 4. Conduct the line test:

5. Subtract the minimum value from all uncovered numbers and add it to the intersection: Student Mon Tue Wed Thurs Fri A 3 2 0 0 0 B 1 3 0 0 3 C 1 0 4 1 4 D 0 4 6 0 0 E 0 0 4 2 1 6.

There are multiple optimal solutions: Solution

Mon

Tue

Wed

Thurs

Fri

1 2 3

E E E

C C C

A B B

B A D

D D A

Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Analytical thinking

14 .

Hours Covered 31 31 31

59) There are 4 jobs in a 4 person office that must be done as quickly as possible. The supervisor has used the assignment method to assign people to jobs, and has completed the first step. She had to rush off to a meeting and has asked to assign the jobs to the people before she returns. The original matrix which shows the expected completion time for each person for each job, and the one she just completed are both shown below. Job A B C D

Ruth 8 13 38 19

Steve 26 28 19 26

Valerie 17 4 18 24

Wayne 11 26 15 10

Job A B C D

Ruth 0 9 23 9

Steve 18 24 4 16

Valerie 9 0 3 14

Wayne 3 22 0 0

Which person should be assigned to which job? How long will the jobs take? Answer: Job Ruth Steve Valerie Wayne A 0 14 9 3 B 9 20 0 22 C 23 0 3 0 D 9 12 14 0 Ruth does job A. Valerie does job B. Steve does job C. Wayne does job D. Total time is 41 minutes. Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Analytical thinking

60) In a transportation problem, items are allocated from sources to destinations at a: A) maximum cost. B) minimum cost. C) minimum profit. D) minimum revenue. Answer: B Diff: 1 Section Heading: The Transportation Model Keywords: transportation problem, objective function, cost minimization AACSB: Application of knowledge

15 .

61) The transportation method assumes that: A) the number of rows is equal to the number of columns. B) there must be at least 2 rows and at least 2 columns. C) both A and B D) the product of rows minus 1 and columns minus 1 should not be less than the number of completed cells. Answer: B Diff: 2 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

62) The transportation method is a linear programming technique where linearity can be found in which of the following ways? A) The cost of goods shipped from any source to any destination is a linear function of quantity shipped. B) The total cost associated with a given plan is a linear function of shipping costs. C) Cell evaluations assume linear movements through the matrix. D) The cost of goods shipped from any source to any destination is a linear function of the cost per unit. Answer: A Diff: 3 Section Heading: The Transportation Model Keywords: transportation method, transportation model AACSB: Application of knowledge

63) Which of the following assumptions is not an assumption of the transportation model? A) Shipping costs per unit are constant. B) There is one transportation route between each source and destination. C) There is one transportation mode between each source and destination. D) Actual total supply and actual total demand must be equal. Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: transportation method, transportation model assumptions AACSB: Application of knowledge

64) The problem that deals with the distribution of goods from several sources to several destinations is the: A) network problem. B) assignment problem. C) transportation problem. D) transshipment problem. Answer: C Diff: 1 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

16 .

65) In the linear programming formulation of a transportation network: A) there is one variable for each arc. B) there is one constraint for each node. C) the sum of variables corresponding to arcs out of an origin node is constrained by the supply at that node. D) all of the above Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: linear programming formulation of a transportation problem AACSB: Application of knowledge

66) Which of the following assumptions is not an assumption of the transportation model? A) Shipping costs are constant. B) There is only one transportation route between source and destination. C) There is only one transportation mode between source and destination. D) Actual supply and actual demand must be equal. Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: transportation method, transportation model assumptions AACSB: Application of knowledge

67) The ________ problem deals with the distribution of goods from several sources to several destinations. A) network B) assignment C) transportation D) transshipment Answer: C Diff: 1 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

68) In a transportation problem, items are allocated from sources to destinations at a ________ cost. A) maximum B) minimum C) high D) low Answer: B Diff: 1 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge

17 .

69) The linear programming model for a transportation problem has constraints for: A) supply at each source. B) supply at each source and demand at each destination. C) demand at each destination. D) a feasible solution. Answer: B Diff: 2 Section Heading: The Transportation Model Keywords: linear programming formulation of a transportation problem AACSB: Application of knowledge

70) In a balanced transportation model where supply equals demand, all constraints are: A) inequalities. B) equalities. C) A and B D) none of the above Answer: B Diff: 2 Section Heading: The Transportation Model Keywords: balanced transportation model, transportation model formulation AACSB: Application of knowledge

71) The supply and demand values along the outside rim of a tableau are called: A) rim requirements. B) rim columns. C) rim rows. D) all of the above Answer: A Diff: 3 Section Heading: The Transportation Model Keywords: rim requirements AACSB: Application of knowledge

72) Which of the following are assumptions or requirements of the transportation problem? A) Minimum quantities must be shipped. B) Shipping costs per unit do not vary with the quantity shipped. C) There can only be one source. D) all of the above Answer: B Diff: 3 Section Heading: The Transportation Model Keywords: assumptions of the transportation problem AACSB: Application of knowledge

18 .

Use the following table and the information to answer the questions below. In the following transportation matrix, all cells except 2C have been evaluated and show no improvement. Evaluate that cell.

73) What is the reduced cost if we decide to allocate to cell 2C? A) -2 B) -1 C) 0 D) +1 E) +2 Answer: A Diff: 2 Section Heading: The Transportation Model Keywords: stepping stone method, reduced cost AACSB: Analytical thinking

74) How many units would be allocated to cell 2C? A) 10 B) 14 C) 6 D) 0 E) 20 Answer: B Diff: 3 Section Heading: The Transportation Model Keywords: stepping stone method, reduced cost AACSB: Analytical thinking

75) Make the necessary allocation to cell 2C and determine the total transportation cost. A) 936 B) 928 C) 908 D) 852 E) 878 Answer: C Diff: 3 Section Heading: The Transportation Model Keywords: stepping stone method AACSB: Analytical thinking

19 .

76) Which of the following are assumptions or requirements of transportation problems? I. Goods are the same from each source. II. There must be a single source. III. Minimum quantities must be shipped. IV. Shipping costs per unit do not vary with the quantity shipped. A) I and III B) I, II, and IV C) I and IV D) II and III Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: transportation problem, assumptions AACSB: Application of knowledge

77) Consider the following transportation tableau which shows the initial solution. Evaluate the cost of allocating units to cell DR.

A) -5 B) -2 C) 0 D) 3 E) 5 Answer: E Diff: 2 Section Heading: The Transportation Model Keywords: stepping stone method, reduced cost AACSB: Analytical thinking

20 .

78) Consider the following transportation tableau which shows the initial solution. Evaluate the cost of allocating units to cell CR.

A) -12 B) -9 C) -6 D) -2 E) +3 Answer: B Diff: 2 Section Heading: The Transportation Model Keywords: stepping stone method, reduced cost AACSB: Analytical thinking

79) An assignment problem is a special form of transportation problem where all supply and demand values equal: A) -1 or 1. B) -1. C) 0. D) 1. Answer: D Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: assignment problem AACSB: Application of knowledge

80) Assignments are made to locations with ________ in the opportunity cost table. A) -1 or 1 B) -1 C) 1 D) 0 Answer: D Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: assignment problem, assignment problem solution procedure AACSB: Application of knowledge

21 .

81) If the number of unique assignments is ________ the number of rows or columns, a line test must be used. A) more than B) less than C) higher than D) equal to Answer: B Diff: 1 Section Heading: Solution of the Assignment Problem Keywords: assignment problem, assignment problem solution procedure AACSB: Application of knowledge

82) A transportation table that has a cell evaluation of 0 means that: A) the table is optimal. B) an equivalent alternative solution exists. C) supply and demand are equal. D) the solution is not optimal. Answer: B Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: transportation table, transportation model solution procedure AACSB: Application of knowledge

83) A transportation table contains an optimal solution when all the empty cell evaluations are: A) positive or 0. B) negative or 0. C) positive. D) negative. Answer: A Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: transportation table, transportation model solution procedure AACSB: Application of knowledge

84) In an assignment problem: A) one agent can do parts of several tasks. B) one task can be done by only one agent. C) each agent is assigned to its own best task. D) all of the above Answer: B Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: assignment problem AACSB: Application of knowledge

22 .

85) The difference between the assignment and the transportation problem is that: A) each supply and demand value is 1 in the assignment problem. B) total supply must equal total demand in the transportation problem. C) the number of origins must equal the number of destinations in the transportation problem. D) all of the above Answer: A Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: assignment and the transportation problems AACSB: Application of knowledge

86) A company that repairs and maintains HVAC systems for businesses wants to assign three service teams to three geographical zones, one team to each zone. Because of the familiarity with each team to the companies located in a zone, there are differences in the efficiencies of each team, reflected in the service costs. The matrix below shows the service costs (in thousands of dollars) for each team in each zone. Assign each team to a zone that minimizes cost.

A) Assign T1 to zone A, T2 to zone B, and T3 to zone C. B) Assign T1 to zone A, T2 to zone C, and T3 to zone B. C) Assign T1 to zone B, T2 to zone A, and T3 to zone C. D) Assign T1 to zone B, T2 to zone C, and T3 to zone A. E) Assign T1 to zone C, T2 to zone A, and T3 to zone B. Answer: C Diff: 3 Section Heading: Solution of the Assignment Problem Keywords: assignment AACSB: Analytical thinking

23 .

Introduction to Management Science, 12e (Taylor) Module C: Integer Programming: The Branch and Bound Method 1) The branch and bound method is a solution approach that partitions the feasible solution space into smaller subsets of solutions. Answer: TRUE Diff: 1 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

2) The branch and bound method is a solution approach that partitions the infeasible solution space into smaller subsets of solutions. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

3) The branch and bound method is a solution technique specifically limited to integer programming problems. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

4) When the branch and bound approach is applied to an integer programming problem, it is used in conjunction with the normal non-integer solution approach. Answer: TRUE Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method, integer programming problem AACSB: Application of knowledge

5) A linear programming model solution with no integer restrictions is called a relaxed solution. Answer: TRUE Diff: 1 Section Heading: Branch and Bound Method Keywords: relaxed solution AACSB: Application of knowledge

6) A linear programming model solution with integer restrictions is called a relaxed solution. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: relaxed solution AACSB: Application of knowledge

1 .

7) The branch and bound method of solving linear integer programming problems is an enumeration method. Answer: TRUE Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

8) The branch and bound solution method cannot be applied to 0-1 integer programming problems. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound solution method, 0-1 integer programming probs AACSB: Application of knowledge

9) Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution. Answer: TRUE Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming, branch and bound method AACSB: Application of knowledge

10) A feasible solution is ensured by rounding down non-integer solution values. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming problems, integer feasible solution AACSB: Application of knowledge

11) A feasible solution is ensured by rounding down integer solution values. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming problems, integer feasible solution AACSB: Application of knowledge

12) A rounded-down integer solution can result in a less than optimal solution. Answer: TRUE Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming problems, integer feasible solution AACSB: Application of knowledge

13) An infeasible solution is ensured by rounding down non-integer solution values. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming problems, integer feasible solution AACSB: Application of knowledge

2 .

14) If an integer programming problem has no feasible solution, then its LP relaxation (relaxed solution) must also have no feasible solution. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: relaxed solution AACSB: Application of knowledge

15) When using branch and bound for a maximization integer programming problem, the lower bound at the initial node can always be determined by rounding down the LP relaxation solution values regardless of the types of constraints in the problem. Answer: FALSE Diff: 3 Section Heading: Branch and Bound Method Keywords: branch and bound method, lower bound AACSB: Application of knowledge

16) The number of nodes considered in a branch and bound tree for maximization integer programming problems is always minimized by going to the node with the largest upper bound. Answer: TRUE Diff: 3 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

17) If an integer linear programming problem has no feasible solution, then its relaxed solution (LP relaxation) must also have no feasible solution. Answer: FALSE Diff: 3 Section Heading: Branch and Bound Method Keywords: relaxed solution, branch and bound method AACSB: Application of knowledge

18) In solving a maximization problem, the optimal profit associated with the relaxed solution (LPrelaxation) is always less than or equal to the value of the optimal profit associated with the integer solution. Answer: FALSE Diff: 2 Section Heading: Branch and Bound Method Keywords: relaxed solution, branch and bound method AACSB: Application of knowledge

19) In using the branch and bound method, if a branch gives an infeasible solution to the associated linear programming problem, then the particular branch is fathomed and is not considered any further. Answer: TRUE Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

3 .

20) In implicit enumeration the feasible integer solutions closest to the optimal non-integer solution are evaluated to see which is best. Answer: FALSE Diff: 1 Section Heading: Branch and Bound Method Keywords: implicit enumeration, integer programming AACSB: Application of knowledge

21) In implicit enumeration, all feasible solutions are evaluated to see which is best. Answer: TRUE Diff: 1 Section Heading: Branch and Bound Method Keywords: implicit enumeration, integer programming AACSB: Application of knowledge

22) Branch and bound cannot be used to solve mixed integer programs. Answer: FALSE Diff: 1 Section Heading: Branch and Bound Method Keywords: branch and bound, mixed integer programs AACSB: Application of knowledge

23) The branch and bound method uses a tree diagram of nodes and branches to organize the solution partitioning. Answer: TRUE Diff: 1 Section Heading: Branch and Bound Method Keywords: branch and bound AACSB: Application of knowledge

24) The ________ method is a solution approach that partitions the feasible solution space into smaller subsets of solutions. Answer: branch and bound Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

25) The ________ integer solution will always be between the upper bound of the relaxed solution and a lower bound of the rounded-down solution. Answer: optimal Diff: 2 Section Heading: Branch and Bound Method Keywords: optimal integer solution, branch and bound method AACSB: Application of knowledge

4 .

26) A linear programming model solution with no integer restrictions is called a ________ solution. Answer: relaxed Diff: 2 Section Heading: Branch and Bound Method Keywords: relaxed solution AACSB: Application of knowledge

27) In using the branch and bound method, we always branch from the node with the ________ upper bound. Answer: maximum Diff: 1 Section Heading: Branch and Bound Method Keywords: branching rule AACSB: Application of knowledge

28) An ________ solution is reached when a feasible integer solution is reached at a node that has an upper bound equal to lower bound. Answer: optimal integer Diff: 2 Section Heading: Branch and Bound Method Keywords: optimal integer solution AACSB: Application of knowledge

29) The branch and bound method can be used for ________ integer problems except only variables with integer restrictions are rounded down to achieve an initial lower bound and only integer variables are branched on. Answer: mixed Diff: 2 Section Heading: Branch and Bound Method Keywords: mixed integer linear programming problems AACSB: Application of knowledge

30) The branch and bound method can be used for 0-1 integer programming problems by adding a ________ 1 constraint for each 0-1 variable. Answer: less-than-or-equal-to Diff: 2 Section Heading: Branch and Bound Method Keywords: 0-1 integer programming, branch and bound method AACSB: Application of knowledge

31) We begin the branch and bound method by first solving the problem as a regular ________ model without integer restrictions. Answer: linear programming Diff: 2 Section Heading: Branch and Bound Method Keywords: relaxed solution, branch and bound method AACSB: Application of knowledge

5 .

32) The branch and bound method uses a tree diagram of ________ and ________ to organize the solution partitioning. Answer: branches, nodes Diff: 1 Section Heading: Branch and Bound Method Keywords: branch and bound AACSB: Application of knowledge

33) The ________ method evaluates all feasible and infeasible solutions to determine the optimal solution. Answer: complete enumeration Diff: 2 Section Heading: Branch and Bound Method Keywords: complete enumeration AACSB: Application of knowledge

34) The ________ method evaluates all feasible solutions to determine the optimal solution. Answer: implicit enumeration Diff: 2 Section Heading: Branch and Bound Method Keywords: implicit enumeration AACSB: Application of knowledge

35) A ________ solution is not guaranteed by rounding down non-integer solution values. Answer: feasible Diff: 1 Section Heading: Branch and Bound Method Keywords: integer feasible solution AACSB: Application of knowledge

36) The production manager for the Rusty soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3 per case and profits for diet soft drink are $2 per case. What are optimal daily profits? Answer: $420 Diff: 3 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Analytical thinking

6 .

37) The production manager for Beer etc. produces two kinds of beer: light and dark. Two of his resources are constrained: malt, of which he can get at most 4800 oz per week; and wheat, of which he can get at most 3200 oz per week. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What are the optimal weekly profits? Answer: $800 Diff: 1 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Analytical thinking

38) Consider a capital budgeting example with five projects from which to select. Let xi = 1 if project a is selected, 0 if not, for i = 1, 2, 3, 4, 5. Write the appropriate constraint(s) for the following condition: If project 3 is chosen, project 4 must be chosen. Answer: x3 - x4 ≤ 0 Diff: 1 Section Heading: Branch and Bound Method Keywords: integer programming formulation AACSB: Analytical thinking

39) Consider a capital budgeting example with five projects from which to select. Let xi = 1 if project a is selected, 0 if not, for i = 1, 2, 3, 4, 5. Write the appropriate constraint(s) for the following condition: If project 1 is chosen, project 5 must not be chosen. Answer: x1 + x5 ≤ 1 Diff: 1 Section Heading: Branch and Bound Method Keywords: integer programming formulation AACSB: Analytical thinking

40) The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same and not all four machines have to be used to produce all of the garden hoses.

This problem requires two different kinds of decision variables. Clearly define each kind. Answer: Xi = the number of hoses produced on machine a Yi = 1 if machine i is used, 0 if not Diff: 1 Section Heading: Branch and Bound Method Keywords: integer programming formulation AACSB: Analytical thinking

7 .

41) The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same and not all four machines have to be used to produce all of the garden hoses.

Give the constraints for the problem. Answer: X1 ≤ 6000 y1 X2 ≤ 7500 y2 X3 ≤ 4000 y3 X4 ≤ 5000 y4 Xi ≥ 10,000 Diff: 1 Section Heading: Branch and Bound Method Keywords: integer programming formulation, constraint formulation AACSB: Analytical thinking

42) The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same and not all four machines have to be used to produce all of the garden hoses.

Write a constraint to ensure that if machine 4 is used, machine 1 will not be used. Answer: y1 + y4 ≤ 1 Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming formulation, constraint formulation AACSB: Analytical thinking

8 .

43) Consider the following integer programming problem. Solve it using the branch and bound method. What are the optimal values of x1, x2 and Z? Maximize

Z = 2x1 + x2

Subject to: 2x1 + 2x2 ≤ 7 4x1 + x2 ≤ 11 x1 and x2 ≥ 0 Answer: x1 = 2, x2 = 1, Z = 5 Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Analytical thinking

44) Solve the following integer linear program using implicit enumeration. MAX

subject to: -

≤ 0.5

≤ 3.5

≥ 0 and integer

Answer: 0 1 2 3 1 2

0 0 0 0 1 1

≤5?

0 -1 -1 -3 0 -1

≤ 3.5 ? 0 1 2 3 2 3

Optimal: x1 = 2, and x2 = 1, and Z = 1 Diff: 2 Section Heading: Branch and Bound Method Keywords: implicit enumeration, integer programming solution AACSB: Analytical thinking

9 .

Z 0 0 0 0 1 1

45) Solve the following integer LP using branch and bound: MAX

subject to:

+ 10

≤ 20

≤2 ,

≥ 0 and integer

Answer: x1 = 0, and x2 = 2, and Z = 10

Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method, integer programming solution AACSB: Analytical thinking

46) Solve the following integer linear program: MAX

subject to: 4 2

≤ 22

≤ 15

≤9

, x ≥ 0, integer Answer: x1 = 4, x2 = 1, Z = 5 Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming solution AACSB: Analytical thinking

10 .

47) Solve the following integer linear program: MAX

subject to: 7

+ +3

integer

≤ 28

≥0

Answer: x1 = 0, x2 = 2, x3 = 6.67, Z = 10.67 Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming solution AACSB: Analytical thinking

48) The branch and bound method is a solution approach that partitions the ________ solution space into smaller subsets of solutions. A) infeasible B) feasible C) optimal D) all of the above Answer: B Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

49) In using rounding of a linear programming model to obtain an integer solution, the solution is: A) always optimal and feasible. B) sometimes optimal and feasible. C) always optimal. D) always feasible. Answer: B Diff: 3 Section Heading: Branch and Bound Method Keywords: branch and bound method, rounded solution AACSB: Application of knowledge

50) The branch and bound method of solving linear integer programming problems is: A) a nonlinear method. B) a relaxation method. C) a graphical solution. D) an enumeration method. Answer: D Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method, integer programming problem AACSB: Application of knowledge

11 .

51) Rounding large values of decision variables to the nearest integer value causes ________ problems than rounding small values. A) more B) fewer C) none of the above Answer: B Diff: 1 Section Heading: Branch and Bound Method Keywords: integer programming solution AACSB: Application of knowledge

52) A linear programming model solution with no integer restrictions is called a(n) ________ solution. A) optimal B) feasible C) relaxed D) all of the above Answer: C Diff: 2 Section Heading: Branch and Bound Method Keywords: relaxed solution AACSB: Application of knowledge

53) The branch and bound method uses a tree diagram of ________ to organize the solution partitioning. A) branches B) nodes C) nodes and branches D) none of the above Answer: C Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound AACSB: Application of knowledge

54) The optimal integer solution will always be between the ________ bound of the relaxed solution and a lower bound of the rounded-down integer solution. A) lower B) optimal C) upper D) all of the above Answer: C Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method, upper bound AACSB: Application of knowledge

12 .

55) The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same and not all four machines have to be used to produce all of the garden hoses.

Write a constraint to ensure that if machine 4 is used, machine 1 will not be used. A) y1 + y4 ≤ 0 B) y1 + y4 ≥ 1 C) y1 + y4 ≤ 1 D) y1 - y4 ≤ 1 E) y1 - y4 ≤ 0 Answer: C Diff: 3 Section Heading: Branch and Bound Method Keywords: integer programming formulation, constraint formulation AACSB: Analytical thinking

56) The optimal integer solution will always be between the upper bound of the ________ solution and a lower bound of the rounded-down ________ solution. A) relaxed, non-integer B) integer, relaxed C) relaxed, integer D) none of the above Answer: C Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming problem, branch and bound method AACSB: Application of knowledge

13 .

57) The upper bound at the initial node of a branch and bound tree is given by A) the value of the objective function of the LP relaxation . B) the value of the objective function after the LP relaxation solution is rounded down to an integer solution. C) the value of the objective function corresponding to an integer feasible solution determined on the basis of trial and error. D) cannot be determined Answer: A Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

58) When using branch and bound to solve an integer programming problem, if the value of X 1 = 2.5 at a given node, then one of the descendant branches would have which one of the additional constraints? A) X1 ≥ 2 B) X1 ≤ 3 C) X1 = 3 D) X1 ≤ 2 E) X1 = 2 Answer: D Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Application of knowledge

59) Consider the following integer programming problem. Solve it using the branch and bound method. What are the optimal values of x1, x2, and Z? Maximize

Z = 2x1 + x2

Subject to: 2x1 + 2x2 ≤ 7 4x1 + x2 ≤ 11 x1 and x2 ≥ 0 A) x1 = 1, x2 = 2, Z = 4 B) x1 = 2, x2 = 1, Z = 5 C) x1 = 1, x2 = 1, Z = 3 D) x1 = 0, x2 = 3, Z = 3 E) x1 = 2, x2 = 2, Z = 6 Answer: B Diff: 2 Section Heading: Branch and Bound Method Keywords: branch and bound method AACSB: Analytical thinking

14 .

60) Which of the following can be used to solve integer programs with 2 variables? I. Graphical techniques II. Complete enumeration III. Relaxed LP solutions IV. Branch and bound A) I, II, III, and IV B) I and III C) I, II, and IV D) I and IV E) I, II and III Answer: C Diff: 1 Section Heading: Branch and Bound Method Keywords: integer prog solution methods, graphic, enumeration, branch/bound AACSB: Application of knowledge

61) Solve the following integer linear program: MAX

Z=2

subject to:

≤7

≤ 11

and

≥0

What are the optimal values of x1 and x2? A) x1 = 1, x2 = 3 B) x1 = 4, x2 = 1 C) x1 = 0, x2 = 3 D) x1 = 3, x2 = 2 E) x1 = 2, x2 = 2 Answer: B Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming solution AACSB: Analytical thinking

15 .

62) Solve the following integer LP using branch and bound: MAX

subject to:

+ 10

≤ 20

≤2 ,

≥ 0 and integer

The optimal value of Z is: A) 7. B) 6. C) 10. D) 11. E) 12. Answer: C Diff: 3 Section Heading: Branch and Bound Method Keywords: integer programming solution AACSB: Analytical thinking

63) Consider the following integer LP. MAX

subject to:

+ 10

≤ 20

≤2 ,

≥ 0 and integer

Solve for the value of x2 at the first node and identify the constraint below that correctly represents one of the descendant branches. A) x2 ≥ 1 B) x2 ≤ 1 C) x2 ≤ 2 D) x2 ≥ 0 Answer: B Diff: 2 Section Heading: Branch and Bound Method Keywords: integer programming solution AACSB: Analytical thinking

16 .

Introduction to Management Science, 12e (Taylor) Module D: Nonlinear Programming: Solution Techniques 1) Linear programming is a special case of nonlinear programming. Answer: TRUE Diff: 1 Section Heading: The Substitution Method Keywords: nonlinear programming AACSB: Application of knowledge

2) The slope of a curve at any point is equal to the derivative of the curves function. Answer: TRUE Diff: 2 Section Heading: The Substitution Method Keywords: derivative of the curve's function, slope of a curve AACSB: Application of knowledge

3) The slope of a curve at its highest point equals 0. Answer: TRUE Diff: 1 Section Heading: The Substitution Method Keywords: slope of a curve AACSB: Application of knowledge

4) The slope of a curve at its highest point equals 1. Answer: FALSE Diff: 1 Section Heading: The Substitution Method Keywords: slope of a curve AACSB: Application of knowledge

5) The derivative of a function equals the slope of the curve defined by that function. Answer: TRUE Diff: 2 Section Heading: The Substitution Method Keywords: derivative of a function AACSB: Application of knowledge

6) In the substitution method, the constraint equation is solved for one variable in terms of another and then substituted into the objective function. Answer: TRUE Diff: 2 Section Heading: The Substitution Method Keywords: substitution method AACSB: Application of knowledge

1 .

7) The Lagrangian function is the original objective function plus the Lagrange multiplier times the difference of the left and right sides of the constraint. Answer: TRUE Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, Lagrangian function AACSB: Application of knowledge

8) In the method of Lagrange multipliers, the model constraints are multiplied by Lagrange multipliers and subtracted from the objective function. Answer: TRUE Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multiplier AACSB: Application of knowledge

9) The Lagrange multiplier is analogous to the dual variables in a linear programming problem. Answer: TRUE Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multiplier AACSB: Application of knowledge

10) The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the quantity value of the constraint equation. Answer: TRUE Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multiplier AACSB: Application of knowledge

11) Lagrange multiplier is another name for shadow price. Answer: TRUE Diff: 1 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multiplier, shadow price AACSB: Application of knowledge

12) The Lagrange multiplier at the optimum gives only the instantaneous rate of change in the objective value. Answer: TRUE Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multiplier AACSB: Application of knowledge

2 .

13) In the method of Lagrange multipliers, constraints as multiples of a multiplier are subtracted from the objective function, which is then differentiated with respect to each variable and solved. Answer: TRUE Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

14) The Lagrangian function is differentiated with respect to each variable, and the resulting equations are solved simultaneously. Answer: TRUE Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

15) The Lagrange multiplier reflects a change in the objective function from a unit change in the righthand-side value of a constraint. Answer: TRUE Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

16) The method of Lagrange multipliers can only be used in solving nonlinear programming problems with one equality constraint. Answer: FALSE Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

17) If a Lagrange multiplier equals 3, a one-unit increase in the right-hand side of a constraint, will result in an increase of 3 in the objective function. Answer: TRUE Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, shadow price AACSB: Application of knowledge

18) In the ________ method, the constraint equation is solved for one variable in terms of another and then substituted into the objective function. Answer: substitution Diff: 1 Section Heading: The Substitution Method Keywords: substitution method AACSB: Application of knowledge

3 .

19) In the method of ________, constraints as multiples of multiplier λ are subtracted from the objective function, which is then differentiated with respect to each variable and solved. Answer: Lagrange multipliers Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

20) The Lagrangian function is ________ with respect to each variable and the resulting equations are solved simultaneously. Answer: differentiated Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, Lagrangian function AACSB: Application of knowledge

21) The Lagrange multiplier, λ, reflects a change in the objective function from a unit change in the ________ value of a constraint. Answer: right-hand-side Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

22) The Lagrangian function is differentiated with respect to each variable and the resulting equations are solved ________ to obtain the value of each variable. Answer: simultaneously Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, Lagrangian function AACSB: Application of knowledge

23) If a nonlinear programming problem results in profit (Z) of $250, and the Lagrange multiplier for a constraint is 5, the new profit will be ________ if the right-hand side of the constraint is decreased by 1 unit. Answer: $255 Diff: 1 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multiplier AACSB: Analytical thinking

24) If total contribution of is expressed as C = 60x1 - 5x12 + 80x2 - 4x22 and x1 = 2x2, then the Lagrangian function is 60x1 - 5x12 + 80x2 - 4x22 ________. Answer: -λ (x1 - 2x2) Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrangian function AACSB: Analytical thinking

4 .

25) If the substitution method cannot be used to solve a nonlinear problem, then the equations which result from taking partial derivatives must be solved using the method of ________. Answer: simultaneous equations Diff: 2 Section Heading: The Substitution Method Keywords: solution of simultaneous equations AACSB: Application of knowledge

26) Given the nonlinear programming model Max Z = 4x 1 - 0.1x1x2 + 5x2 - 0.2 x22 Subject to: x1 + 2x2 = 4 What is the Lagrangian function? Answer: 4x1 - 0.1x1x2 + 5x2 - 0.2x22 - λ(x1 + 2x2 - 40) Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Analytical thinking

27) Given the nonlinear programming model Max Z = 5x1 - 2x2- 3x22 Subject to: x1 + 4x2 = 6 What is the Lagrangian function? Answer: 5x1 - 2x2+-3x22- λ (x1+4x2 - 6) Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Analytical thinking

28) Given the nonlinear programming model Max Z = 5x1 - 2x22 Subject to: x1 + 4x2 = 6 What is the Lagrangian function? Answer: 5x1 - 2x22 + - λ (x1 + 4x2 - 6) Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Analytical thinking

29) Given the nonlinear programming model Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What is the Lagrangian function? Answer: 5x1 - 2x22 - λ ( x1+x2 -6) Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Analytical thinking

5 .

30) Given the nonlinear programming model Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What are the optimal values of x1 and x2? Answer: x1 = 4.75, x2 = 1.25 Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, solution of simultaneous equations AACSB: Analytical thinking

31) Given the nonlinear programming model Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What is the optimal profit? Answer: Z = 20.625 Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, solution of simultaneous equations AACSB: Analytical thinking

32) Given the nonlinear programming model Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What is the optimal value of the Lagrange multiplier? Answer: λ = 5 Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, solution of simultaneous equations AACSB: Analytical thinking

33) Write the Lagrangian function for the following nonlinear program: Min x12 + 2x22 - 8x1 - 12x2 + 34 subject to: x12 + 2x22 = 5 Answer: L = x12 + 2x22 - 8x1 - 12x2 + 34 - λ (x12 + 2x22 - 5) Diff: 1 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrangian function AACSB: Analytical thinking

6 .

34) Solve the following nonlinear program: Min x12 + 2x22 - 8 x1 - 12x2 + 34 subject to: x12 + 2x22 = 5 Answer: λ = -1.6, x1 = 1.54, x2 = 1.15 Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrangian multipliers, solution AACSB: Analytical thinking

35) A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 - 5x1, and the per unit contribution for the cocktail glasses (x2) is 80 - 4x2 for a total contribution of 60x1 - 5x12 + 80x2 - 4x22. Demand requires that the production of juice glasses is twice the production of cocktail glasses.(x1 = 2x2). What is the Lagrangian function for this problem? Answer: L = 60x1 - 5x12 + 80x2 - 4x22 - λ (x1 - 2x2) Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrangian function AACSB: Analytical thinking

36) A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 - 5x1, and the per unit contribution for the cocktail glasses (x2) is 80 - 4 x2 for a total contribution of 60 x1 - 5x12 + 80x2 - 4x22. Demand requires that the production of juice glasses is twice the production of cocktail glasses (x1 = 2x2). Write the objective function for this problem which illustrates the technique of substitution. Answer: 20x2 - 24x22 or 100x1 - 6x12 Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: solution to constrained nonlinear program AACSB: Analytical thinking

37) The slope of a curve at its highest point equals: A) 0. B) 1. C) 2. D) 3. Answer: A Diff: 2 Section Heading: The Substitution Method Keywords: substitution method, slope of a curve AACSB: Application of knowledge

7 .

38) The slope of a curve at any point is ________ the derivative of the curves function. A) smaller than B) larger than C) equal to D) none of the above Answer: C Diff: 2 Section Heading: The Substitution Method Keywords: substitution method, derivative of the function AACSB: Application of knowledge

39) The least complex method for solving nonlinear programming problems is referred to as: A) the substitution method. B) Lagrange multipliers. C) nonlinear programming. D) none of the above Answer: A Diff: 1 Section Heading: The Substitution Method Keywords: substitution method AACSB: Application of knowledge

40) The ________ method for solving nonlinear programming problems is referred to as substitution. A) least complex B) most complex C) most difficult D) least difficult Answer: A Diff: 3 Section Heading: The Substitution Method Keywords: substitution method AACSB: Application of knowledge

41) The derivative of a function ________ the slope of the curve defined by that function. A) is larger than B) equals C) is smaller than D) is similar to Answer: B Diff: 2 Section Heading: The Substitution Method Keywords: derivative of a function AACSB: Application of knowledge

8 .

42) In the substitution method, the constraint equation is solved for one variable ________ and then substituted into the objective function. A) only B) after another C) at a time D) in terms of another Answer: D Diff: 2 Section Heading: The Substitution Method Keywords: substitution method AACSB: Application of knowledge

43) The Lagrangian function is differentiated with respect to each variable, and the resulting equations are solved: A) in the order of the variables. B) one after the other. C) one at a time. D) simultaneously. Answer: D Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

44) In the method of Lagrange multipliers, the model constraints are multiplied by Lagrange multipliers and ________ the objective function. A) divided by B) multiplied by C) added to D) subtracted from Answer: D Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

45) The Lagrange multiplier is ________ the dual variables in a linear programming problem. A) analogous to B) contradictory to C) inversely related to D) the opposite of Answer: A Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Application of knowledge

9 .

46) Given the nonlinear programming model: Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What are the optimal values of x1 and x2? A) x1 = 4.75, x2 = 1.25 B) x1 = 5.00, x2 = 3.25 C) x1 = 4.50, x2 = 2.25 D) x1 = 4.50, x2 = 1.25 E) x1 = 5.75, x2 = 0.75 Answer: A Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, solution of simultaneous equations AACSB: Analytical thinking

47) Given the nonlinear programming model: Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What is the optimal value of the Lagrange multiplier? A) λ = 1 B) λ = 2 C) λ = 3 D) λ = 4 E) λ = 5 Answer: E Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, solution of simultaneous equations AACSB: Analytical thinking

10 .

48) Given the nonlinear programming model: Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What is the optimal value of the objective function? A) Z = 19.625 B) Z = 20.625 C) Z = 21.625 D) Z = 22.625 E) Z = 23.625 Answer: B Diff: 3 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers, solution of simultaneous equations AACSB: Analytical thinking

49) Solving nonlinear optimization problems using Lagrange multipliers requires: A) calculus. B) algebra. C) computers. D) A and B E) A and C Answer: D Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multipliers AACSB: Analytical thinking

50) A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x2 - 10C2 + 40Cx + 120x - 200C + 600. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, which of these methods represents the simplest way to determine the optimal number of square feet of shelf space for the product? A) Lagrangian functions B) Excel Solver C) substitution method D) solution of simultaneous equations E) none of the above Answer: C Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: solution methods AACSB: Analytical thinking

11 .

51) The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the ________ of the constraint equation. A) coefficient B) objective function C) right-hand side D) shadow price Answer: C Diff: 2 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrange multiplier AACSB: Application of knowledge

52) Consider the following objective function and constraint: C(x) = 2x12 - 15x + 3x23 - 9x2 + 30, such that x1 = 3x2. Which of the following is the correct Lagrangian function? A) L = 2x12 - 15x + 3x23 - 9x2 + 30 - λ (3x2 - x1) B) L = 2x12 - 15x + 3x23 - 9x2 + 30 - λ (x2 - 3x1) C) L = 2x12 - 15x + 3x23 - 9x2 + 30 - λ (3x1 - x2) D) L = 2x12 - 15x + 3x23 - 9x2 + 30 - λ (3x2 - 3x1) Answer: C Diff: 1 Section Heading: The Method of Lagrange Multipliers Keywords: Lagrangian function AACSB: Analytical thinking

12 .

Introduction to Management Science, 12e (Taylor) Module E: Game Theory 1) Game theory addresses decision situations with two or more decision makers in competition. Answer: TRUE Diff: 1 Section Heading: Game Theory Keywords: game theory AACSB: Application of knowledge

2) Game theory addresses decision situations with two or fewer decision makers in competition. Answer: FALSE Diff: 1 Section Heading: Game Theory Keywords: game theory AACSB: Application of knowledge

3) A two-person game encompasses two players. Answer: TRUE Diff: 1 Section Heading: Types of Game Situations Keywords: two-person game AACSB: Application of knowledge

4) In a zero-sum game, one player's gains represent another's exact losses. Answer: TRUE Diff: 2 Section Heading: Types of Game Situations Keywords: zero-sum game AACSB: Application of knowledge

5) In a game situation, it is assumed that the payoff table is known to all players. Answer: TRUE Diff: 2 Section Heading: Types of Game Situations Keywords: payoff table AACSB: Application of knowledge

6) A strategy is a plan of action followed by a player. Answer: TRUE Diff: 2 Section Heading: Types of Game Situations Keywords: strategy AACSB: Application of knowledge

7) In a strategy it is assumed that the payoff table is known to all players. Answer: FALSE Diff: 2 Section Heading: Types of Game Situations Keywords: strategy, payoff table AACSB: Application of knowledge

1 .

8) The value of the game is the offensive player's gain and the defensive player's loss in a zero-sum game. Answer: TRUE Diff: 2 Section Heading: Types of Game Situations Keywords: value of the game AACSB: Application of knowledge

9) The value of the game is the defensive player's gain and the offensive player's loss in a zero-sum game. Answer: FALSE Diff: 2 Section Heading: Types of Game Situations Keywords: value of the game AACSB: Application of knowledge

10) The best strategy for each player is his or her optimal strategy. Answer: TRUE Diff: 1 Section Heading: Types of Game Situations Keywords: strategy AACSB: Application of knowledge

11) The payoffs for a mixed strategy game assumes that the game is played exactly one time. Answer: FALSE Diff: 1 Section Heading: Types of Game Situations Keywords: mixed strategy AACSB: Application of knowledge

12) The payoffs for a mixed strategy game assumes that the game is played many times. Answer: TRUE Diff: 2 Section Heading: Types of Game Situations Keywords: mixed strategy AACSB: Application of knowledge

13) In a mixed strategy game, players switch decision in response to the other player. Answer: TRUE Diff: 1 Section Heading: Types of Game Situations Keywords: mixed strategy AACSB: Application of knowledge

14) In a pure strategy game, each player adopts a single strategy as an optimal strategy. Answer: TRUE Diff: 1 Section Heading: A Pure Strategy Keywords: pure strategy game AACSB: Application of knowledge

2 .

15) With the minimax criterion, each player seeks to minimize maximum possible losses. Answer: TRUE Diff: 2 Section Heading: A Pure Strategy Keywords: minimax criterion AACSB: Application of knowledge

16) A point of equilibrium is a value that is simultaneously the minimum of a row and the maximum of a column. Answer: TRUE Diff: 1 Section Heading: A Pure Strategy Keywords: pure strategy, equilibrium point AACSB: Application of knowledge

17) A point of equilibrium is a value that is simultaneously the maximum of a row and the minimum of a column. Answer: FALSE Diff: 1 Section Heading: A Pure Strategy Keywords: pure strategy, equilibrium point AACSB: Application of knowledge

18) In a ________ game one player's gains represent another player's exact losses. Answer: zero-sum Diff: 1 Section Heading: Types of Game Situations Keywords: zero-sum game AACSB: Application of knowledge

19) A ________ is a plan of action followed by a player. Answer: strategy Diff: 2 Section Heading: Types of Game Situations Keywords: game theory, strategy AACSB: Application of knowledge

20) In a ________ game each player adopts a single strategy as an optimal strategy. Answer: pure strategy Diff: 1 Section Heading: A Pure Strategy Keywords: pure strategy game AACSB: Application of knowledge

21) A ________ game occurs when each player selects an optimal strategy that does not result in an equilibrium point when the minimax criterion is used. Answer: mixed strategy Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy game AACSB: Application of knowledge

3 .

22) In a pure strategy game the optimal strategy for each player results in the same payoff, called an ________ point. Answer: equilibrium or saddle Diff: 2 Section Heading: A Pure Strategy Keywords: pure strategy game, equilibrium point AACSB: Application of knowledge

23) In a(n) ________ game, players switch decisions in response to the decision of the other player and eventually return to the initial decisions, resulting in a closed loop. Answer: mixed strategy Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy game AACSB: Application of knowledge

24) In the expected ________ method, a plan of strategies is determined by each player so that expected gain of one equals the expected loss of the other. Answer: gain and loss Diff: 2 Section Heading: A Mixed Strategy Keywords: expected gain and loss method AACSB: Application of knowledge

25) A strategy is ________ and can be eliminated if all its payoffs are worse than the corresponding payoffs for another strategy. Answer: dominated Diff: 2 Section Heading: A Pure Strategy Keywords: dominated strategies AACSB: Application of knowledge

26) In game theory, each player seeks to minimize maximum possible losses with the ________ criterion. Answer: minimax Diff: 2 Section Heading: A Pure Strategy Keywords: minimax criterion AACSB: Application of knowledge

27) A pure strategy game can be solved according to the ________ criterion. Answer: minimax Diff: 1 Section Heading: A Pure Strategy Keywords: minimax AACSB: Application of knowledge

4 .

28) A(n) ________ occurs when the optimal strategy for each player results in the same payoff. Answer: equilibrium or saddle point Diff: 2 Section Heading: A Pure Strategy Keywords: pure strategy, equilibrium point AACSB: Application of knowledge

29) The ________ method uses probabilities to determine the best strategy for each player. Answer: gain and loss Diff: 2 Section Heading: A Mixed Strategy Keywords: expected gain and loss AACSB: Application of knowledge

30) The ________ for a mixed strategy game assumes that the game is played many times. Answer: payoffs Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy, payoff AACSB: Application of knowledge

31) Given the following payoff table:

1 2

A 20 4

B 10 15

What is the value of the game? Answer: 12.38 Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy AACSB: Analytical thinking

Use the following table to answer the question(s) below. s1

32) What decision should be made by the optimistic decision maker? Answer: d2 Diff: 3 Section Heading: A Mixed Strategy Keywords: maximax criterion AACSB: Analytical thinking

5 .

33) What decision should be made by the conservative decision maker? Answer: d3 Diff: 3 Section Heading: A Mixed Strategy Keywords: maximin criterion AACSB: Analytical thinking

34) What decision should be made under minimax regret? Answer: 3-way tie Diff: 3 Section Heading: A Mixed Strategy Keywords: minimax regret criterion AACSB: Analytical thinking

35) If the probabilities of s1, s2, and s3 are 0.2, 0.4, and 0.4, respectively, then what decision should be made under expected value? Answer: Ev(d1) = 7.6 Ev(d2) = 9.6 (best) Ev(d3) = 8.2 Diff: 3 Section Heading: A Mixed Strategy Keywords: expected value criterion AACSB: Analytical thinking

Use the following table to answer the question(s) below. s1

250

750

500

300

-250

1200

500

600

36) What decision should be made by the conservative decision maker? Answer: D3 Diff: 3 Section Heading: A Mixed Strategy Keywords: maximin criterion AACSB: Analytical thinking

37) What decision should be made under minimax regret? Answer: D3 Diff: 3 Section Heading: A Mixed Strategy Keywords: minimax criterion AACSB: Analytical thinking

6 .

38) If the probabilities of d1, d2, and d3 are 0.2, 0.5, and 0.3, respectively, then what decision should be made under expected value? Answer: Ev(d1) = 575 (best) Ev(d2) = 295 Ev(d3) = 530 Diff: 3 Section Heading: A Mixed Strategy Keywords: expected value criterion AACSB: Analytical thinking

The local operations manager for the IRS must decide whether to hire one, two, or three temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code.

39) If he uses the maximin criterion, how many new workers will he hire? Answer: 1 Diff: 2 Section Heading: A Mixed Strategy Keywords: maximin criterion AACSB: Analytical thinking

40) If he uses the minimax regret criterion, how many new workers will he hire? Answer: 2 Diff: 2 Section Heading: A Mixed Strategy Keywords: minimax regret criterion AACSB: Analytical thinking

41) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what are the expected net revenues for the number of workers he will decide to hire? Answer: Hire 1 worker (50 > 48 > 46), net revenue = $50. Diff: 2 Section Heading: A Mixed Strategy Keywords: expected value criterion AACSB: Analytical thinking

7 .

Mary Schultz is the incumbent senator from Ohio and John Henderson is her opponent in the upcoming election. Since Mr. Henderson is seeking to unseat Ms. Schultz, he is on the offensive, while Ms. Schultz hopes to minimize his gains or her losses in the election. The following payoff table shows the various percentage point gains/losses in the polls for the two candidates based on their selection of certain political strategies.

42) Based on the information above, use the expected gain and loss method and determine the probability that each strategy will be used by each player. Answer: Probability that John Henderson uses strategy 1 is 50%. Probability that John Henderson uses strategy 2 is 50%. Probability that Mary Schultz uses strategy A is 87.5%. Probability that Mary Schultz uses strategy B is 12.5%. Diff: 3 Section Heading: A Mixed Strategy Keywords: mixed strategy AACSB: Analytical thinking

43) Based on the information above, use the expected gain and loss method and determine the equilibrium point. Answer: 6.5 Diff: 3 Section Heading: A Mixed Strategy Keywords: expected gain and loss method, equilibrium point, mixed strategy AACSB: Analytical thinking

44) Mary Schultz is the incumbent Senator from Ohio and John Henderson is her opponent in the upcoming election. Since Mr. Henderson is seeking to unseat Ms. Schultz, he is on the offensive, while Ms. Schultz hopes to minimize his gains or her losses in the election. The following payoff table shows the various percentage point gains/losses in the polls for the two candidates based on their selection of certain political strategies.

Determine the optimal strategy and the optimal payoff for both players. Answer: John, strategy 2; Mary strategy A; and the optimal payoff = 6 Diff: 2 Section Heading: A Mixed Strategy Keywords: pure strategy AACSB: Analytical thinking

8 .

45) Given the following payoff/loss table for a mixed strategy game between two players:

Identify dominated strategy(s), if it (they) exist(s). Answer: B dominates A, B dominates D, 2 dominates 4 Diff: 2 Section Heading: A Mixed Strategy Keywords: dominating strategies AACSB: Analytical thinking

46) Construct the payoff matrix for the game, "rock, paper, scissors" for 2 players, A and B. Assume that "paper covers rock," "rock breaks scissors," and "scissors cut paper." If player A wins, assign +1. If player A loses, assign -1. Answer:

Diff: 1 Section Heading: A Mixed Strategy Keywords: payoff matrix AACSB: Analytical thinking

9 .

Two companies are about to make a decision regarding an investment in a new promotional campaign. Company A will either advertise in all media or advertise in newspapers only. Company B will either run a sweepstake or run a big sale. The payoff matrix is shown below.

47) Using the information above, determine the proportion of time that each company should employ each strategy. Answer: Company A: Adopt A1 strategy 3/8 of the time and alternative A2 5/8 of the time. Company B: Adopt B1 25% of the time and B2 75% of the time. Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy, expected gain/loss method, equilibrium point AACSB: Analytical thinking

48) Using the information above, determine the value of the game. Answer: 0.25 Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy, value of the game AACSB: Analytical thinking

49) In order to attract listeners, a radio station gives away money if listeners correctly identify the amount of money found by a "treasure hunter". A contestant would guess the amount on the air, and the disc jockey would then play a tape in which the "treasure hunter" said how much he had found. If the caller guessed correctly, they won the amount of money found by the treasure hunter. If they guessed incorrectly, they received nothing. Suppose that the treasure hunter either found $50 or $100. The payoff matrix represents this game:

If the station plans on running the game every day for 10 days, how much will they pay out? Answer: Value of the game is $33.33 per game, for $333.33 for the ten-day period. Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy, value of the game AACSB: Analytical thinking

10 .

50) In a zero sum game, one player's gains represent another's exact: A) gains. B) losses. C) gains and losses. D) gains or losses. Answer: B Diff: 2 Section Heading: Game Theory Keywords: zero-sum game AACSB: Application of knowledge

51) The ________ is the offensive player's gain and the defensive player's loss in a zero-sum game. A) game situation B) value of the game C) strategy D) best strategy E) pure strategy Answer: B Diff: 2 Section Heading: Game Theory Keywords: value of the game AACSB: Application of knowledge

52) A ________ is a plan of action followed by a player. A) game situation B) strategy C) value of the game D) best strategy E) pure strategy Answer: B Diff: 2 Section Heading: Game Theory Keywords: strategy AACSB: Application of knowledge

53) Game theory assumes that players behave: A) logically. B) emotionally. C) rationally. D) A, B, and C E) A and B Answer: E Diff: 2 Section Heading: Game Theory Keywords: game theory assumptions AACSB: Application of knowledge

11 .

54) The ________ criterion results in the maximum of the minimum payoffs. A) minimax B) maximax C) maximin D) minimin Answer: C Diff: 2 Section Heading: Game Theory Keywords: maximin criterion AACSB: Application of knowledge

55) Regret is the difference between the payoff from the: A) best decision and all other decision payoffs. B) worst decision and all other decision payoffs. C) best decision and the worst decision payoffs. D) none of the above Answer: A Diff: 2 Section Heading: Game Theory Keywords: regret, minimax regret criterion AACSB: Application of knowledge

56) Determining the worst payoff for each alternative and choosing the alternative with the best of the worst payoffs is called a ________ criterion. A) maximin B) minimin C) maximax D) minimax Answer: A Diff: 3 Section Heading: Game Theory Keywords: maximin criterion AACSB: Application of knowledge

57) The maximin approach to decision making refers to: A) minimizing the maximum return. B) maximizing the minimum return. C) maximizing the maximum return. D) minimizing the minimum return. Answer: B Diff: 3 Section Heading: Game Theory Keywords: maximin criterion AACSB: Application of knowledge

12 .

58) With the ________ criterion each player seeks to minimize maximum possible losses. A) minimax B) maximax C) minimin D) maximin Answer: A Diff: 1 Section Heading: Game Theory Keywords: minimax criterion AACSB: Application of knowledge

59) A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a: A) decision tree. B) payoff table. C) feasible region. D) payback matrix. Answer: B Diff: 2 Section Heading: A Mixed Strategy Keywords: payoff table AACSB: Application of knowledge

60) The expected value and expected opportunity loss criteria result in: A) the same decision. B) different decisions. C) similar decisions. D) all of the above Answer: A Diff: 1 Section Heading: A Mixed Strategy Keywords: expected value criterion, expected opportunity loss criterion AACSB: Application of knowledge

61) A(n) ________ game occurs when each player selects an optimal strategy that does not result in an equilibrium point when the minimax criterion is used. A) optimal strategy B) pure strategy C) mixed strategy D) best strategy Answer: C Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy AACSB: Application of knowledge

13 .

62) Based on the information above, determine the proportion of time that Company A should employ each strategy. A) A1: 12.5%, A2: 87.5% B) A1: 25%, A2: 75% C) A1: 37.5%, A2: 62.5% D) A1: 50%, A2: 50% E) A1: 62.5%, A2: 37.5% Answer: C Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy, expected gain/loss method, equilibrium point AACSB: Analytical thinking

63) Based on the information above, determine the proportion of time that Company B should employ each strategy. A) B1: 12.5%, B2: 87.5% B) B1: 25%, B2: 75% C) B1: 37.5%, B2: 62.5% D) B1: 50%, B2: 50% E) B1: 62.5%, B2:37.5% Answer: B Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy, expected gain/loss method, equilibrium point AACSB: Analytical thinking

14 .

64) In order to attract listeners, a radio station gives away money if listeners correctly identify the amount of money found by a "treasure hunter". A contestant would guess the amount on the air, and the disc jockey would then play a tape in which the "treasure hunter" said how much he had found. If the caller guessed correctly, they won the amount of money found by the treasure hunter. If they guessed incorrectly, they received nothing. Suppose that the treasure hunter either found $50 or $100. The payoff matrix represents this game:

If the station plans on running the game every day for 10 days, how much will they pay out? A) $250 B) $333 C) $500 D) $750 E) $667 Answer: B Diff: 2 Section Heading: A Mixed Strategy Keywords: mixed strategy, value of the game AACSB: Analytical thinking

15 .

Introduction to Management Science, 12e (Taylor) Module F: Markov Analysis 1) Markov analysis is a probabilistic technique. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis, probabilistic technique AACSB: Application of knowledge

2) Markov analysis is not a probabilistic technique. Answer: FALSE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

3) Markov analysis does not provide a recommended decision. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

4) Markov analysis provides a recommended decision. Answer: FALSE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

5) Markov analysis is not an optimization technique. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

6) Markov analysis is an optimization technique. Answer: FALSE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

7) Markov analysis is a descriptive technique that results in probabilistic information. Answer: TRUE Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

1 .

8) Markov analysis is not a descriptive technique that results in probabilistic information. Answer: FALSE Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

9) The brand-switching problem analyzes the probability of customers' changing brands of a product over time. Answer: TRUE Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: brand-switching problem, Markov analysis AACSB: Application of knowledge

10) Markov analysis provides information on the probability of customers switching from one brand to one or more other brands. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: brand-switching problem, Markov analysis AACSB: Application of knowledge

11) A Markov assumption is that the probabilities in each row sum to 1 because they are mutually exclusive and collectively exhaustive. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis assumptions AACSB: Application of knowledge

12) A Markov assumption is that the probabilities apply to all system participants. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis assumptions AACSB: Application of knowledge

13) A Markov assumption is that the probabilities are constant over time. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis assumptions AACSB: Application of knowledge

14) A Markov assumption is that the probabilities change over time. Answer: FALSE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis assumptions AACSB: Application of knowledge

2 .

15) The state of the system is where the system is at a point in time. Answer: TRUE Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis, state of the system AACSB: Application of knowledge

16) If a Markov process contains an absorbing state, the process will eventually terminate in the absorbing state. Answer: TRUE Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: absorbing states AACSB: Application of knowledge

17) Markov analysis can be used to determine the steady state probabilities associated with machine breakdowns. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis, steady state AACSB: Application of knowledge

18) Decision trees can be used to solve for steady state probabilities. Answer: TRUE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: decision trees, Markov process, steady state AACSB: Application of knowledge

19) Markov Analysis always results in a steady state. Answer: FALSE Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis, steady state AACSB: Application of knowledge

20) A transition matrix cannot cause the system to cycle between states. Answer: FALSE Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: transition matrix, cyclic behavior AACSB: Application of knowledge

21) Markov analysis is a ________ technique. Answer: probabilistic or descriptive Diff: 1 Section Heading: Introduction Keywords: Markov analysis, probabilistic technique AACSB: Application of knowledge

3 .

22) An assumption of Markov analysis is that the probability of moving from a state to all other states sum to ________. Answer: 1 (one) Diff: 1 Section Heading: Introduction Keywords: assumptions of Markov analysis AACSB: Application of knowledge

23) An assumption of Markov analysis is that the probabilities are ________ over time. Answer: constant Diff: 3 Section Heading: Introduction Keywords: assumptions of Markov analysis AACSB: Application of knowledge

24) A ________ is the probability of moving from one state to another during one time period. Answer: transition probability Diff: 3 Section Heading: The Characteristics of Markov Analysis Keywords: Markov Analysis, assumption of Markov analysis AACSB: Application of knowledge

25) The probability of ending up in a state in the future is ________ of the starting state. Answer: independent Diff: 2 Section Heading: Steady-State Probabilities Keywords: Markov analysis, assumptions of Markov analysis AACSB: Application of knowledge

26) ________ probabilities are average constant probabilities that the system will be in a state in the future. Answer: Steady-state Diff: 2 Section Heading: Steady-State Probabilities Keywords: steady state probabilities AACSB: Application of knowledge

27) In Markov analysis, once the system leaves a(n) ________ state, it will never return. Answer: transient Diff: 2 Section Heading: Special Types of Transition Matrices Keywords: transient state AACSB: Application of knowledge

28) In Markov analysis, once the system moves into a(n) ________ state, it is trapped and cannot leave. Answer: absorbing Diff: 2 Section Heading: Special Types of Transition Matrices Keywords: absorbing states AACSB: Application of knowledge

4 .

29) A transition matrix is ________ when it moves back and forth between states. Answer: cyclic Diff: 2 Section Heading: Special Types of Transition Matrices Keywords: cyclic transition matrix AACSB: Application of knowledge

30) A Markov assumption is that the probabilities in each row sum to ________ because they are mutually exclusive and collectively exhaustive. Answer: 1 (one) Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis assumptions AACSB: Application of knowledge

31) Steady state probabilities can be computed by developing a set of equations using ________ operations and solving them simultaneously. Answer: matrix Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: Markov process, steady state AACSB: Application of knowledge

32) A common application of Markov analysis is ________. Answer: brand switching, machine breakdowns, accounts receivable, promotion/graduation Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: applications of Markov processes AACSB: Application of knowledge

33) Although information from Markov analysis can be obtained using a ________, it is time-consuming and cumbersome. Answer: decision tree Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: decision trees AACSB: Application of knowledge

34) In certain applications, the transition matrix may first need to be divided into submatrices. The identity matrix, I, and matrix Q (the nonabsorbing matrix) are then used to determine the ________ matrix. Answer: fundamental Diff: 2 Section Heading: Special Types of Transition Matrices Keywords: fundamental matrix AACSB: Application of knowledge

5 .

35) A Markov process for two states has the following transition matrix:

A B

A 0.35 0.42

B 0.65 0.58

Assume that we start with state 1, what is the probability matrix of the system being in state A or B in period 3 given the system started in state B? Answer: 0.3955; 0.6045 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov process, Markov analysis, state probability calculations AACSB: Analytical thinking

36) A Markov process has the following transition matrix:

A B

A 0.25 0.60

B 0.75 0.40

What are the steady state probabilities? Answer: 0.444; 0.556 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov process, steady state probability AACSB: Analytical thinking

37) A Markov process has the following transition matrix:

A B

A 0.90 0.70

B 0.10 0.30

What are the steady state probabilities? Answer: 0.875; 0.125 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov process, steady state probability AACSB: Analytical thinking

6 .

38) A Markov process has the following transition matrix:

A B

A 0.65 0.45

B 0.35 0.55

What are the steady state probabilities? Answer: 0.563; 0.437 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov process, steady state probability AACSB: Analytical thinking

The only car dealership in a community stocks cars from two manufacturers, Fret and Cessy. The following transition matrix shows the probabilities of a customer purchasing each brand of car in the next year given that he or she purchased that car in the current year.

39) Given that a customer purchased the brand Fret in the present year (year 1), determine the probability that a customer will purchase Cessy in year 3. Answer: .39 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: transition probability matrix AACSB: Analytical thinking

40) Given that a customer purchased the brand Cessy in the present year (year 1), determine the probability that a customer will purchase Fret in year 3. Answer: .52 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: transition probability matrix AACSB: Analytical thinking

41) Given that a customer purchased the brand Cessy in the present year (year 1), determine the probability that a customer will purchase Cessy in year 3. Answer: .48 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: transition probability matrix AACSB: Analytical thinking

7 .

42) Determine the steady state probabilities for Fret and Cessy. Answer: .571, .429 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: steady state probabilities AACSB: Analytical thinking

43) For the following transition matrices, determine the transient or absorbing states.

Answer: State 2 is absorbing. Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: absorbing states AACSB: Analytical thinking

44) For the following transition matrices, determine the transient or absorbing states.

Answer: State 1 is transient. Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: transient state AACSB: Analytical thinking

8 .

45) Participants eligible for a retraining program can be in one of four states: A - not in the training program B - discharged C - in training D - employed Given the following transition matrix, determine the fundamental matrix.

Answer: F=

Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov process, fundamental matrix AACSB: Analytical thinking

9 .

46) Participants eligible for a retraining program can be in one of four states: A - not in the training program B - discharged C - in training D - employed You are given the following transition matrix and the fundamental matrix.

Assume that there were initially 10 people not in the training program (State A) and 60 people who were in the training program (State C). How many people will end up being discharged, and how many people will be employed? Answer: F×R=

Total in B = 10 (.92) + 60 (.77) = 55.4 discharged Total in D = 10 (.08) + 60 ( .23) = 14.6 employed Diff: 3 Section Heading: The Characteristics of Markov Analysis Keywords: F X R matrix, solutions AACSB: Analytical thinking

47) The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week.

If there are 2000 customers who shop at either store, how many over the long run would shop at Limmer's? Answer: 0.333 × 2000 = 667 Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Analytical thinking

10 .

48) Limmer's is going to launch a new advertising campaign in order to attract new customers. The "before" and "after" transition matrices are shown below:

Before:

After:

If there are 1000 customers who shop at these two stores, how many customers, over the long run, will switch to Limmer's as a result of the new campaign? Answer: Before: 0.333 × 2000 = 667 , After: 0.43 × 2000 = 860, representing an increase of 193 people. Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Analytical thinking

49) Markov analysis ________ a recommended decision. A) does not provide B) always provides C) sometimes provides D) rarely provides Answer: A Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

50) A Markov assumption is that the probabilities ________ over time. A) become smaller B) become larger C) change D) are constant Answer: D Diff: 3 Section Heading: The Characteristics of Markov Analysis Keywords: Markov assumption AACSB: Application of knowledge

11 .

51) A Markov assumption is that the probabilities apply to ________ system participants. A) none of the B) the major C) some D) all Answer: D Diff: 3 Section Heading: The Characteristics of Markov Analysis Keywords: Markov assumption AACSB: Application of knowledge

52) Markov analysis is a ________ technique that results in ________ information. A) descriptive, descriptive B) probabilistic, descriptive C) descriptive, probabilistic D) probabilistic, probabilistic Answer: C Diff: 3 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis AACSB: Application of knowledge

53) Which of the following is not an assumption or a characteristic of a Markov Process? A) The transition probabilities are the same for any customer. B) The transition probabilities will remain constant over time. C) The probability of being in a particular state at any one time period depends only on the state immediately preceding it. D) In a transition matrix, sum of the row probabilities must sum to one. E) In a transition matrix, sum of the column probabilities must sum to one. Answer: E Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov analysis assumptions AACSB: Application of knowledge

54) A Markov assumption is that the probabilities in each row sum to 1 because they are: A) mutually exclusive. B) collectively exhaustive. C) mutually exclusive and collectively exhaustive. D) mutually exclusive or collectively exhaustive. Answer: C Diff: 2 Section Heading: The Characteristics of Markov Analysis Keywords: Markov assumption AACSB: Application of knowledge

12 .

55) The ________ is the probability of moving from one state to another during one time period. A) transition probability B) state of the system C) steady-state probabilities D) transition matrix Answer: A Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: transition probability AACSB: Application of knowledge

56) The ________ is where the system is at a point in time. A) transition probability B) state of the system C) steady-state probabilities D) transition matrix Answer: B Diff: 1 Section Heading: The Characteristics of Markov Analysis Keywords: state of the system AACSB: Application of knowledge

57) For the following transition matrices, what is the absorbing state(s)?

A) state 1 B) state 2 C) state 3 D) state 4 E) state 2 and 4 Answer: B Diff: 2 Section Heading: The Transition Matrix Keywords: absorbing states AACSB: Analytical thinking

13 .

The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week.

58) If a customer shopped at Don's the first week, what is the probability that they are shopping at Limmer's the third week? A) 0.17 B) 0.34 C) 0.66 D) 0.83 E) none of the above Answer: A Diff: 2 Section Heading: The Transition Matrix Keywords: transition probability matrix AACSB: Analytical thinking

59) If there are 2000 customers who shop at either store, how many over the long run would shop at Limmer's? A) 333 B) 400 C) 667 D) 1000 E) 1600 Answer: C Diff: 2 Section Heading: Steady-State Probabilities Keywords: steady state AACSB: Analytical thinking

60) The ________ is average, constant probability that the system will be in a state in the future. A) transition probability B) state of the system C) steady-state probability D) transition matrix Answer: C Diff: 1 Section Heading: Steady-State Probabilities Keywords: steady state probabilities AACSB: Application of knowledge

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61) Given that a customer purchased the brand Fret in the present year (year 1), determine the probability that a customer will purchase Cessy in year 3. A) .7 B) .61 C) .39 D) .21 E) .18 Answer: C Diff: 2 Section Heading: Steady-State Probabilities Keywords: transition probability matrix AACSB: Analytical thinking

62) Determine the steady state probabilities for Fret and Cessy. A) .875, .125 B) .645, .355 C) .621, .379 D) .571, .429 E) .55, .45 Answer: D Diff: 2 Section Heading: Steady-State Probabilities Keywords: steady state probabilities AACSB: Analytical thinking

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Use the following information to answer the question(s) below. Participants eligible for a retraining program can be in one of four states: A - not in the training program B - discharged C - in training D - employed You are given the following transition matrix and the fundamental matrix.

63) Assume that there were initially 10 people not in the training program (State A) and 60 people who were in the training program (State C). Approximately how many people will end up being discharged? A) 10 B) 15 C) 40 D) 55 E) 60 Answer: D Diff: 3 Section Heading: Steady-State Probabilities Keywords: steady state AACSB: Analytical thinking

64) Assume that there were initially 10 people not in the training program (State A) and 60 people who were in the training program (State C). Approximately how many people will be employed? A) 10 B) 15 C) 40 D) 55 E) 60 Answer: B Diff: 2 Section Heading: Steady-State Probabilities Keywords: steady state AACSB: Analytical thinking

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