MAT 540 Quiz 3. 20/20. Get an A++. - 63159

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Question 1

 

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

certainty.

 

Question 2

 

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

 

Question 3

 

The following inequality represents a resource constraint for a maximization problem:

X + Y . 20

 

Question 4

 

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

 

Question 5

 

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

 

Question 6

 

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

 

Question 7

 

A feasible solution violates at least one of the constraints.

 

Question 8

 

Decision variables

 

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 points are not feasible?

 

Question 11

 

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?

 

Question 12

 

Which of the following could be a linear programming objective function?

 

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 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 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?

 

Question 15

 

The linear programming problem:

MIN Z = 2x1 + 3x2

Subject to: x1 + 2x2 . 20

5x1 + x2 . 40

4x1 +6x2 . 60

x1 , x2 . 0 ,

 

Question 16

 

Which of the following statements is not true?

 

Question 17

 

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 18

 

Consider the following minimization problem:

Min z = x1 + 2x2

s.t. x1 + x2 . 300

2x1 + x2 . 400

2x1 + 5x2 . 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

 

Question 19

 

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

 

Question 20

 

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.

Solution Description

Question 1

 

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

certainty.

 

Question 2

 

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

 

Question 3

 

The following inequality represents a resource constraint for a maximization problem:

X + Y . 20

 

Question 4

 

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

 

Question 5

 

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

 

Question 6

 

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

 

Question 7

 

A feasible solution violates at least one of the constraints.

 

Question 8

 

Decision variables

 

Question 9

 

The following is a

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