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## `MAT540/MAT 540 WEEK 7 QUIZ

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MAT 540 WEEK 7 In minimization LP problems the feasible region is always below the resource constraints. Answer Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Answer In a linear programming problem, all model parameters are assumed to be known with certainty. Answer A linear programming problem may have more than one set of solutions. Answer If the objective function is parallel to a constraint, the constraint is infeasible. Answer If the objective function is parallel to a constraint, the constraint is infeasible. Answer Surplus variables are only associated with minimization problems. Answer ) Which of the following could be a linear programming objective function? Answer 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? Answer 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? Answer 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 storage space constraint? Answer 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? Answer 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? Answer 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? Answer 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: Answer Decision variables Answer In a linear programming problem, a valid objective function can be represented as Answer Solve the following graphically Max z = 3×1 +4×2 s.t. x1 + 2×2 â‰¤ 16 2×1 + 3×2 â‰¤ 18 x1 â‰¥ 2 x2 â‰¤ 10 x1, x2 â‰¥ 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 Answer Consider the following linear programming problem: Max Z = \$15x + \$20y Subject to: 8x + 5y â‰¤ 40 0.4x + y â‰¥ 4 x, y â‰¥ 0 At the optimal

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