# Mat540 quiz 3 | Mathematics homework help

Quiz 3

Question 1

Surplus variables are only associated with minimization problems.

Question 2

A feasible solution violates at least one of the constraints.

Question 3

A linear programming model consists of only decision variables and constraints.

Question 4

Graphical solutions to linear programming problems have an infinite number of possible objective function lines.

Question 5

If the objective function is parallel to a constraint, the constraint is infeasible.

Question 6

A linear programming problem may have more than one set of solutions.

Question 7

In minimization LP problems the feasible region is always below the resource constraints.

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 labeled Z*.  This linear programming problem is a:

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 constraints has a surplus greater than 0?

Question 11

Which of the following statements is not true?

Question 12

Decision variables

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 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 14

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. 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

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 17

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?

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 answer in decimal notation.

Question 19

Solve the following graphicallyMax z = 3×1 +4×2 s.t. x1 + 2×2 ≤ 16 2×1 + 3×2 ≤ 18 x1 ≥ 2 x2 ≤ 10 x1, x2 ≥ 0Find 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 20

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. 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

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