MATH 540 Week 6 Quiz 3
download Question 1 1. The following inequality represents a resource constraint for a maximization problem: X + Y ≼ 20 Answer True False 2 points Question 2 1. Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Answer True False 2 points Question 3 1. A feasible solution violates at least one of the constraints. Answer True False 2 points Question 4 1. A linear programming problem may have more than one set of solutions. Answer True False 2 points Question 5 1. A linear programming model consists of only decision variables and constraints. Answer True False 2 points Question 6 1. In minimization LP problems the feasible region is always below the resource constraints. Answer True False 2 points Question 7 1. Surplus variables are only associated with minimization problems. Answer True False 2 points Question 8 1. 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 maximum profit? Answer $25000 $35000 $45000 $55000 $65000 2 points Question 9 1. The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeledZ*.
This linear programming problem is a: Answer maximization problem minimization problem irregular problem cannot tell from the information given 2 points Question 10 1. The production manager for the Coory soft drink company is considering the production of 2 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 her 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? Answer only time only syrup time and syrup neither time nor syrup 2 points Question 11 1. The linear programming problem: MIN Z = Subject to:
2x1 + 3x2 x1 + 2x2 ≤ 20 5x1 + x2 ≤ 40 4x1 +6x2 ≤ 60 x1 , x2 ≥ 0 ,
Answer has only one solution. has two solutions. has an infinite number of solutions. does not have any solution. 2 points Question 12 1. ) Which of the following could be a linear programming objective function? Answer Z = 1A + 2BC + 3D Z = 1A + 2B + 3C + 4D Z = 1A + 2B / C + 3D all of the above
2 points Question 13 1. Decision variables Answer measure the objective function measure how much or how many items to produce, purchase, hire, etc. always exist for each constraint measure the values of each constraint 2 points Question 14 1. In a linear programming problem, a valid objective function can be represented as Answer Max Z = 5xy Max Z 5x2 + 2y2 Max 3x + 3y + 1/3z Min (x1 + x2) / x3 2 points Question 15 1. The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeledZ*.
Which of the following points are not feasible? Answer A J H G 2 points Question 16 1. 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 Point Point Point Point
B C D E
2 points Question 17 1. The production manager for the Coory soft drink company is considering the production of 2 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 her 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? Answer MAX $4D MAX $2D MAX $2R MAX
$2R + $3R + $3D + $4D +
$2R 2 points Question 18 1. Consider the following minimization problem: Min z = x1 + 2x2 s.t. x1 + x2 ≥ 300 2x1 + x2 ≥ 400 2x1 + 5x2 ≤ 750 x1, x2 ≥ 0 Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Answer 2 points Question 19 1. Solve the following graphically Max z = 3x1 +4x2 s.t. x1 + 2x2 ≤ 16 2x1 + 3x2 ≤ 18 x1 ≥ 2 x2 ≤ 10 x1, x2 ≥ 0 Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Answer 2 points Question 20 1. 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 be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation. Answer · Question 1 2 out of 2 points The following inequality represents a resource constraint for a maximization problem: X + Y ≥ 20
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Question 2 2 out of 2 points
Graphical solutions to linear programming problems have an infinite number of possible objective function lines.
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Question 3 2 out of 2 points
A feasible solution violates at least one of the constraints.
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Question 4 2 out of 2 points
A linear programming problem may have more than one set of solutions.
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Question 5 2 out of 2 points
A linear programming model consists of only decision variables and constraints.
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Question 6 2 out of 2 points
In minimization LP problems the feasible region is always below the resource constraints. Answer ·
Question 7 2 out of 2 points
Surplus variables are only associated with minimization problems. Answer ·
Question 8 2 out of 2 points
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 maximum profit? Answer ·
Question 9 2 out of 2 points
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*.
This linear programming problem is a: Answer ·
Question 10 2 out of 2 points
The production manager for the Coory soft drink company is considering the
production of 2 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 her 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? Answer ·
Question 11 2 out of 2 points
The linear programming problem: MIN Z = Subject to:
2x1 + 3x2 x1 + 2x2 ≤ 20 5x1 + x2 ≤ 40 4x1 +6x2 ≤ 60 x1 , x2 ≥ 0 ,
Answer ·
Question 12 2 out of 2 points
) Which of the following could be a linear programming objective function? Answer ·
Question 13 2 out of 2 points
Decision variables Answer ·
Question 14 2 out of 2 points
In a linear programming problem, a valid objective function can be represented as Answer ·
Question 15 2 out of 2 points
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*.
Which of the following points are not feasible? Answer ·
Question 16 2 out of 2 points
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 ·
Question 17 2 out of 2 points
The production manager for the Coory soft drink company is considering the production of 2 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 her 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? Answer ·
Question 18 2 out of 2 points
Consider the following minimization problem: Min z = x1 + 2x2 s.t. x1 + x2 ≥ 300 2x1 + x2 ≥ 400 2x1 + 5x2 ≤ 750 x1, x2 ≥ 0 Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Answer ·
Question 19 0 out of 2 points
Solve the following graphically Max z = 3x1 +4x2 s.t. x1 + 2x2 ≤ 16 2x1 + 3x2 ≤ 18 x1 ≥ 2 x2 ≤ 10 x1, x2 ≥ 0 Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Answer ·
Question 20 2 out of 2 points
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 be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation. Answer