# MAT540 - Quiz 3 - A Graded Solution - 41130

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### ·         Question 1

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

### ·         Question 2

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

### ·         Question 3

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

### ·         Question 4

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

### ·         Question 5

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

### ·         Question 6

 The following inequality represents a resource constraint for a maximization problem:                                                                  X + Y ≥ 20

### ·         Question 7

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

### ·         Question 8

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

### ·         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?
 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 11

 In a linear programming problem, the binding constraints for the optimal solution are:  Which of these objective functions will lead to the same optimal solution?

### ·         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*.  This linear programming problem is a:
 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?

### ·         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 maximum profit?

### ·         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

 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 17

 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 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.

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