# MATH 540 quiz 3 (7) New Work

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**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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