# MAT 540 WEEK 7 QUIZ 3 Week Quiz

Question 1

In a linear programming problem, all model parameters are assumed to be known with certainty.

True

False

Question 2

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

True

False

Question 3

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

True

False

Question 4

Surplus variables are only associated with minimization problems.

True

False

Question 5

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

True

False

Question 6

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

True

False

Question 7

A feasible solution violates at least one of the constraints.

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?

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?

\$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:

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?

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:

5×1 + 3×2 ≤ 30

2×1 + 5×2 ≤ 20

Which of these objective functions will lead to the same optimal solution?

2×1 + 1×2

7×1 + 8×2

80×1 + 60×2

25×1 + 15×2

Question 13

In a linear programming problem, a valid objective function can be represented as

Max Z = 5xy

Max Z 5×2 + 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?

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?

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:

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?

2R + 5D ≤ 480

2D + 4R ≤ 480

2R + 3D ≤ 480

2R + 4D ≤ 480

Question 18

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. 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 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?

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?

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