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MATH 540 quiz 3 (7) NEW

Question 1

A linear programming model consists of only decision variables and constraints.

Question 2

In a linear programming problem, all model parameters are assumed to be known with certainty.

Question 3

A linear programming problem may have more than one set of solutions.

Question 4

In minimization LP problems the feasible region is always below the resource constraints.

Question 5

A feasible solution violates at least one of the constraints.

Question 6

If the objective function is parallel to a constraint, the constraint is infeasible.

Question 7

Graphical solutions to linear programming problems have an infinite number of possible objective function lines.

Question 8

) Which of the following could be a linear programming objective function?

Question 9

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 the limited resources are production time (8 hours = 480 minutes per day) and syrup 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?

Question 10

In a linear programming problem, a valid objective function can be represented as

Question 11

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?

Question 12

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 constraints has a surplus greater than 0?

Question 13

Which of the following statements is not true?

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. What is the objective function?

Question 15

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?

Question 16

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*.

The equation for constraint DH is:

Question 17

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?

Question 18

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   in decimal notation.

Evaluation Method Correct  Case Sensitivity
Exact Match -1.5
Exact Match - 1.5

Question 19

Max Z =    \$3x + \$9y
Subject to:       20x + 32y ≤ 1600
4x + 2y ≤ 240
y ≤ 40
x, y ≥ 0
At the optimal solution, what is the amount of slack associated with the second constraint?

Evaluation Method Correct  Case Sensitivity
Exact Match 96

Question 20

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   will be an integer. Please give your   as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25

Evaluation Method Correct  Case Sensitivity
Exact Match 27

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