At the optimal solution what is the amount of slack

Question

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

• True
• False

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

• True
• False

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

• True
• False

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

• True
• False

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

• True
• False

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

• True
• False

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

• True
• 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.  (graph did not copy/paste) Which of the following constraints has a surplus greater than 0?

• BF
• CG
• DH
• 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?

• $25000
• $35000
• $45000
• $55000
• $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. graph did not copy/paste The equation for constraint DH is:

• 4X + 8Y ≥ 32
• 8X + 4Y ≥ 32
• X + 2Y ≥ 8
• 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?

• only time
• only syrup
• time and syrup
• neither time nor syrup

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

5x1 + 3x2 ≤ 30
2x1 + 5x2 ≤ 20

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

• 2x1 + 1x2
• 7x1 + 8x2
• 80x1 + 60x2
• 25x1 + 15x2

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

• Max Z = 5xy
• Max Z 5x2 + 2y2
• Max 3x + 3y + 1/3z
• 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?

• MAX Z = $300B + $100 M
• MAX Z = $300M + $150 B
• MAX Z = $300B + $150 M
• 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.  graph did not copy/paste If this is a maximization, which extreme point is the optimal solution?

• Point B
• Point C
• Point D
• 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 labeled.  This linear programming problem is a:

• maximization problem
• minimization problem
• irregular problem
• 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?

• 2R + 5D ≤ 480
• 2D + 4R ≤ 480
• 2R + 3D ≤ 480
• 2R + 4D ≤ 480

Question 18: 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?

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?

Question 20: Consider the following linear programming problem:

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

At the optimal solution, what is the amount of slack associated with the first constraint?