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. 

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

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