MATH 540 Week 11 Final Exam 2
download • Question 1 5 out of 5 points In general, an increase in price increases the break even point if all costs are held constant. Answer
• Question 2
The feasible solution area contains infinite solutions to the linear program.
• Question 3 5 out of 5 points A change in the value of an objective function coefficient will always change the value of the optimal solution. Answer
• Question 4 • When using a linear programming model to solve the “diet” problem, the objective is generally to maximize nutritional content. Answer
• Question 5 5 out of 5 points 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 can not be selected. Answer
• Question 6 5 out of 5 points In a transshipment problem, items may be transported from destination to destination and from source to source. Answer
• Question 7 5 out of 5 points
The events in an experiment are mutually exclusive if only one can occur at a time. Answer
• Question 8 5 out of 5 points The minimax criterion minimizes the maximum payoff. Answer
• Question 9 5 out of 5 points Excel can be used to simulate systems that can be represented by both discrete and continuous random variables. Answer
• Question 10 5 out of 5 points A cycle is an up and down movement in demand that repeats itself in less than 1 year. Answer
• Question 11 5 out of 5 points A bed and breakfast even every month if they book 30 rooms over the course of a month. Their fixed cost is $6000 per month and the revenue they receive from each booked room is $180. What is the variable cost per occupied room? Answer
• Question 12 5 out of 5 points If the price decreases but fixed and variable costs do not change, the break even point Answer
• Question 13 Cully furniture buys 2 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 $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function? Answer
• Question 14
Cully furniture buys 2 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 $75000 to invest in shelves this week, and the warehouse has 18000 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? Answer
• Question 15 5 out of 5 points The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem: The Answer Report:
• Question 16 5 out of 5 points Given the following linear programming problem that minimizes cost. Min Z = 2x + 8y Subject to 8x + 4y ≥ 64 2x + 4y ≥ 32 y≥2 What is the sensitivity range for the third constraint, y ≥ 2? Answer
• Question 17 0 out of 5 points Compared to blending and product mix problems, transportation problems are unique because Answer
• Question 18 5 out of 5 points Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 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. Answer
• Question 19 5 out of 5 points If we are solving a 0-1 integer programming problem, the constraint x1 =x2 is a __________ constraint. Answer
• Question 20 5 out of 5 points
The Wiethoff Company has a contract to produce garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used. Answer
• Question 21 5 out of 5 points The assignment problem constraint x31+x32+x33+x34 ≤ 2 means Answer
• Question 22 The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.
The constraint that represents the quantity supplied by DC 1 is: Answer
• Question 23 5 out of 5 points 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 percentage of the students will take between 2 and 6 minutes to find a parking spot in the main parking lot. Answer
• Question 24
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? Answer
• Question 25 5 out of 5 points 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 conservative strategy is: Answer
• Question 26 5 out of 5 points 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: Answer
• Question 27 5 out of 5 points 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 10minute intervals. Based on 100 tenminute intervals, the following probability distribution and random number assignments developed. Number of Arrivals 6 7 8 9 10
Probability
Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period? Answer
• Question 28
For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:
Answer
• Question 29 5 out of 5 points 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? Answer
• Question 30 5 out of 5 points Consider the following graph of sales.
Which of the following characteristics is exhibited by the data? Answer
• Question 31 5 out of 5 points A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Find the breakeven point. Answer
• Question 32
Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.
Formulation: Let
x = number of tractors produced per period y = number of lawn mowers produced per period
MAX 30x + 30y subject to 2 x + y ≤ 60 2 x + 3y ≤ 120 x ≤ 45 x, y ≥ 0 The graphical solution is shown below.
What is the shadow price for fabrication? Write your answers with two
significant places after the decimal and do not include the dollar “$” sign. Answer
• Question 33 5 out of 5 points Consider the following linear program, which maximizes profit for two products, regular (R), and super (S): MAX 50R + 75S s.t. 1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R + 0.5 S ≤ 300 paint (hours) .16R + 0.4 S ≤ 100 inspection (hours) Sensitivity Report: Cell $B$7 $C$7
Name Regular = Super =
Cell
Name Assembly $E$3 (hr/unit) $E$4 Paint (hr/unit) $E$5 Inspect (hr/unit)
If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign. Answer
• Question 34
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 optimal cost of this plan? Write your answers with two significant places after the decimal and do not include the dollar “$” sign. Answer: 3.50 (tolerance: ± 0) Chapter 4 Answer
• Question 35
Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer. MAX Z = 5x1 + 8x2 s.t. x1 + x2 ≤ 6 5x1 + 9x2 ≤ 45 x1, x2 ≥ 0 and integer Answer
• Question 36
A life insurance company wants to estimate their 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? Round your result to four significant places after the decimal. Answer
• Question 37 5 out of 5 points Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.
Answer
• Question 38 5 out of 5 points An investor is consider 4 different opportunities, A, B, C, or D. The payoff for
each opportunity will depend on the economic conditions, represented in the payoff table below.
Investment A B C D
Poor (S1) 50 80 -100 25
Economic Condition Average Good (S2) (S3) 75 20 15 40 300 -50 25 25
Excellent (S4) 30 50 10 25
Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Round up your answer to the nearest integer. Answer
• Question 39 5 out of 5 points The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? Do not include the dollar “$” sign with your answer.
Answer
• Question 40
The following sales data are available for 2003-2008 : Year 2003 2004 2005 2006 2007 2008
Calculate the MAPD and express it in decimal notation. Use four significant digits after the decimal. Answer