# Question 1 In a linear programming problem, all model parameters are assumed to be known with certainty. Question 2 A linear programming problem may have more than one set of

Question 1 In a linear programming problem, all model parameters are assumed to be known with certainty. Question 2 A linear programming problem may have more than one set of solutions. Question 3 The following inequality represents a resource constraint for a maximization problem: X + Y . 20 Question 4 In minimization LP problems the feasible region is always below the resource constraints. Question 5 If the objective function is parallel to a constraint, the constraint is infeasible. Question 6 If the objective function is parallel to a constraint, the constraint is infeasible. Question 7 A feasible solution violates at least one of the constraints. Question 8 Decision variables 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*. The equation for constraint DH is: 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 labeled Z*. Which of the following points are not feasible? Question 11 In a linear programming problem, the binding constraints for the optimal solution are: 5×1 + 3×2 . 30 2×1 + 5×2 . 20 Which of these objective functions will lead to the same optimal solution? Question 12 Which of the following could be a linear programming objective function? Question 13 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 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. is the objective function? 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. is the objective function? Question 15 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 16 Which of the following statements is not true? Question 17 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 18 Consider the following minimization problem: Min z = x1 + 2×2 s.t. x1 + x2 . 300 2×1 + x2 . 400 2×1 + 5×2 . 750 x1, x2 . 0 Find the optimal solution. is the value of the objective function at the optimal solution? Note: The answer will be an integer. give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Question 19 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. is the value of the objective function at the optimal solution? Note: The answer will be an integer. give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Question 20 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. would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation.