06 Jun MAT 540 Week 7 Quiz 3 Set 1 QUESTIONS NEW
uestion 1: Graphical solutions to linear programming problems have an infinite number of possible objective function lines.
Question 2: The following inequality represents a resource constraint for a maximization problem:
X + Y ≥ 20
Question 3: In minimization LP problems the feasible region is always below the resource constraints.
Question 4: In a linear programming problem, all model parameters are assumed to be known with certainty.
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: If the objective function is parallel to a constraint, the constraint is infeasible.
Question 8: 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 9: 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?
Question 10: 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 11: 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 12: Which of the following statements is not true?
Question 13: In a linear programming problem, a valid objective function can be represented as
Question 14: The linear programming problem:
MIN Z = 2×1 + 3×2
Subject to: x1 + 2×2 ≤ 20
5×1 + x2 ≤ 40
4×1 +6×2 ≤ 60
x1 , x2 ≥ 0 ,
Question 15: 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:
Question 16: 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 maximization, which extreme point is the optimal solution?
Question 17: Which of the following could be a linear programming objective function?
Question 18: Solve the following graphically
Max z = 3×1 +4×2
s.t. x1 + 2×2 ≤ 16
2×1 + 3×2 ≤ 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
Question 19: 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?
Question 20: 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?
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