MAT 540 WEEK 7 QUIZ 3 (A++++ GUARANTEE) 20/20 - 88507

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Question 1 In a linear programming problem, all model parameters are assumed to be known with certainty. Answer True False Question 2 Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Answer True False Question 3 In minimization LP problems the feasible region is always below the resource constraints. Answer True False Question 4 Surplus variables are only associated with minimization problems. Answer True False Question 5 If the objective function is parallel to a constraint, the constraint is infeasible. Answer True False Question 6 A linear programming model consists of only decision variables and constraints. Answer True False Question 7 A feasible solution violates at least one of the constraints. Answer 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? Answer 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? Answer \$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: Answer 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? Answer 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? Answer 2x1 + 1x2 7x1 + 8x2 80x1 + 60x2 25x1 + 15x2 Question 13 In a linear programming problem, a valid objective function can be represented as Answer 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? Answer 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? Answer 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 labeledZ*. graph did not copy/paste This linear programming problem is a: Answer 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? Answer 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? 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 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? Answer 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? Answer
Solution Description

Question 1
In a linear programming problem, all model parameters are assumed to be known with certainty.
Answer
True
False
Question 2
Graphical solutions to linear programming problems have an infinite number of possible objective function lines.
Answer
True
False
Question 3
In minimization LP problems the feasible region is always below the resource constraints.
Answer
True
False
Question 4
Surplus variables are only associated with minimization problems.
Answer
True
False
Question 5
If the objective function is parallel to a constraint, the constraint is infeasible.
Answer
True
False
Question 6
A linear programming model consists of only decision variables and constraints.
Answer
True
False
Question 7
A feasible solution violates at least one of the constraints.
Answer
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

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