# Mat 540 week 7 quiz 3 week quiz question 1 in a linear programming

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:

5×1 + 3×2 ≤ 30

2×1 + 5×2 ≤ 20

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

Answer

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

Answer

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?

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 = 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

Answer

27

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

96

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

0

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