Value of the objective function at the optimal solution

Question

Assignment:

Question 1. In a linear programming problem, all model parameters are assumed to be known with certainty.

1. True
2. False

Question 2. Graphical solutions to linear programming problems have an infinite number of possible objective function lines.

1. True
2. False

Question 3. In minimization LP problems the feasible region is always below the resource constraints.

1. True
2. False

Question 4. Surplus variables are only associated with minimization problems.

1. True
2. False

Question 5. If the objective function is parallel to a constraint, the constraint is infeasible.

1. True
2. False

Question 6. A linear programming model consists of only decision variables and constraints.

1. True
2. False

Question 7. A feasible solution violates at least one of the constraints.

1. True
2. False

Question 8. 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 constraints has a surplus greater than 0?

1. BF
2. CG
3. DH
4. AJ

Question 9. 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?

1. $25000
2. $35000
3. $45000
4. $55000
5. $65000

Question 10. 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*.

The equation for constraint DH is:

1. 4X + 8Y ≥ 32
2. 8X + 4Y ≥ 32
3. X + 2Y ≥ 8
4. 2X + Y ≥ 8

Question 11. 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?

1. only time
2. only syrup
3. time and syrup
4. neither time nor syrup

Question 12. In a linear programming problem, the binding constraints for the optimal solution are:

1. 5x1 + 3x2 ≤ 30
2. 2x1 + 5x2 ≤ 20

Which of these objective functions will lead to the same optimal solution?

1. 2x1 + 1x2
2. 7x1 + 8x2
3. 80x1 + 60x2
4. 25x1 + 15x2

Question 13. In a linear programming problem, a valid objective function can be represented as

1. Max Z = 5xy
2. Max Z 5x2 + 2y2
3. Max 3x + 3y + 1/3z
4. Min (x1 + x2) / x3

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?

1. MAX Z = $300B + $100 M
2. MAX Z = $300M + $150 B
3. MAX Z = $300B + $150 M
4. MAX Z = $300B + $500 M

Question 15. 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?

1. Point B
2. Point C
3. Point D
4. Point E

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 labeledZ*.

This linear programming problem is a:

1. maximization problem
2. minimization problem
3. irregular problem
4. cannot tell from the information given

Question 17. 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?

1. 2R + 5D ≤ 480
2. 2D + 4R ≤ 480
3. 2R + 3D ≤ 480
4. 2R + 4D ≤ 480

Question 18. Solve the following graphically

1. Max z = 3x1 +4x2
2. s.t. x1 + 2x2 ≤ 16
3. 2x1 + 3x2 ≤ 18
4. x1 ≥ 2
5. x2 ≤ 10
6. 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.

Question 19. Max Z = $3x + $9y Subject to:

1. 20x + 32y ≤ 1600
2. 4x + 2y ≤ 240
3. y ≤ 40
4. x, y ≥ 0

Question 20. Consider the following linear programming problem:

1. Max Z = $15x + $20y
2. Subject to: 8x + 5y ≤ 40
3. 0.4x + y ≥ 4
4. x, y ≥ 0