Deck 21: Supplement Operational Decision-Making Tools: Linear Programming

Question 1

The objective function in a linear programming formulation defines the feasible solution space.

Answer 1

False

Question 2

The objective function is a linear relationship that either minimizes or maximizes some value.

Answer 2

True

Question 3

TicToc produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $3000 and a maximum of 1000 hours of labor per week.Each A produced generates $35.00 in profit for the company.Each B produced generates $25.00 in profit for the company.The company's objective function is

A)Maximize Z = $35.00A + $25.00B.
B)Minimize Z = $12A + 8B.
C)Minimize Z = 4A + 3B.
D)None of these answer choices is correct.

Answer 3

A

Question 4

Most real-world linear programming problems cannot be solved graphically.

Question 5

The formulation for a linear programming problem cannot include more than one decision variable.

Question 6

Linear programming problems with three decision variables can be solved graphically.

Question 7

Atlas Inc.produces product A and product B.Each product must go through two processes.Each A produced requires two hours in process 1 and five hours in process 2.Each B produced requires six hours in process 1 and three hours in process 2.There are 80 hours of capacity available each week in each process.Each A produced generates $6.00 in profit for the company.Each B produced generates $9.00 in profit for the company.The company's objective function is

A)Maximize Z = $6.00A + $9.00B.
B)Maximize Z = $9.00A + $6.00B.
C)Minimize Z = $6.00A + $9.00B.
D)Minimize Z = $6.00A +$9.00B.

Question 8

Linear programming is a mathematical modeling technique based on linear relationships

Question 9

The optimal solution for a linear programming problem will always occur at an extreme point.

Question 10

While all linear programming problems have a single objective function,very few,if any,have constraints.

Question 11

Operations mangers find very few types of linear program models applicable today because finding an optimal solution is no longer a concern.

Question 12

_____________ represent a restriction on decision variable values for a linear programming problem.

A)Surpluses
B)Constraints
C)Extreme points
D)Optimal points

Question 13

A formulation for a linear programming model consists of a decision variable,a constraint and several objective functions.

Question 14

Because linear programming provides an optimal solution,sensitivity analysis is never an important consideration.

Question 15

In general,the objective function for linear programming problems in operations is one of minimizing costs.

Question 16

A linear programming model's constraints are nonlinear relationships that describe the restrictions placed on the decision variables.

Question 17

The simplex method used for solving linear programming problems uses matrix algebra to solve simultaneous equations.

Question 18

The feasible solution space contains the values for the decision variables that satisfy the linear programming model's constraints.

Question 19

Atlas Inc.produces product A and product B.Each product must go through two processes.Each A produced requires two hours in process 1 and five hours in process 2.Each B produced requires six hours in process 1 and three hours in process 2.There are 80 hours of capacity available each week in each process.Each A produced generates $6.00 in profit for the company.Each B produced generates $9.00 in profit for the company.The capacity constraint for Process 2 is

A)5A + 3B > 80
B)6A + 3 B < 80
C)5A + 3B < 80
D)5A + 3B < 80

Question 20

Atlas Inc.produces product A and product B.Each product must go through two processes.Each A produced requires two hours in process 1 and five hours in process 2.Each B produced requires six hours in process 1 and three hours in process 2.There are 80 hours of capacity available each week in each process.Each A produced generates $6.00 in profit for the company.Each B produced generates $9.00 in profit for the company.The constraint for process 1 is represented by

A)2A + 5B < 80.
B)2A + 6B > 80.
C)2A + 6B < 80.
D)2A + 6B < 80.

Question 21

A company produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $5000 and a maximum of 800 hours of labor per week.Each A produced generates $45.00 in profit for the company.Each B produced generates $35.00 in profit for the company.The labor constraint is represented by

A)45A + 35B < 800.
B)45A + 35B > 800.
C)4A + 5B > 800.
D)4A + 5B < 800.

Question 22

Briefly define the components that comprise a linear programming model.

Question 23

A company produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $5000 and a maximum of 800 hours of labor per week.Each A produced generates $45.00 in profit for the company.Each B produced generates $35.00 in profit for the company.The objective function for this company is represented by

A)Min 4A + 5B.
B)Max 8A + 6B.
C)Min 45A + 35B.
D)Max 45A + 35B.

Question 24

For a less than or equal to (<)constraint the shadow price represents the

A)amount you would be willing to pay for one additional unit of a resource.
B)amount you at which you would be willing to sell one additional unit of a resource.
C)difference between the slack price and the surplus price.
D)difference between the surplus price and the slack price.

Question 25

Atlas Inc.produces product A and product B.Each product must go through two processes.Each A produced requires two hours in process 1 and five hours in process 2.Each B produced requires six hours in process 1 and three hours in process 2.There are 80 hours of capacity available each week in each process.Each A produced generates $6.00 in profit for the company.Each B produced generates $9.00 in profit for the company.If the company produces 6 units of A and 9 units of B the amount of slack (in hours)for process 1 is

A)0 hours.
B)14 hours.
C)66 hours.
D)80 hours.

Question 26

The constraint 3x1 + 6x2 > 48 is converted to an equality by

A)adding a slack variable.
B)subtracting a surplus variable.
C)adding both a slack variable and a surplus variable.
D)subtracting both a slack variable and a surplus variable.

Question 27

TicToc produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $3000 and a maximum of 1000 hours of labor per week.Each A produced generates $35.00 in profit for the company.Each B produced generates $25.00 in profit for the company.If the company produces 100 units of A and 200 units of B the amount of slack (in hours)for labor is

A)0 hours.
B)14 hours.
C)66 hours.
D)80 hours.

Question 28

TicToc produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $3000 and a maximum of 1000 hours of labor per week.Each A produced generates $35.00 in profit for the company.Each B produced generates $25.00 in profit for the company.The constraint for the budget is represented by

A)$35A + $25B < $3,000.
B)$35A + $25B > $3,000.
C)$12A + $8B > $3,000.
D)$12A + $8B < $3,000.

Question 29

Atlas Inc.produces product A and product B.Each product must go through two processes.Each A produced requires two hours in process 1 and five hours in process 2.Each B produced requires six hours in process 1 and three hours in process 2.There are 80 hours of capacity available each week in each process.Each A produced generates $6.00 in profit for the company.Each B produced generates $9.00 in profit for the company.If the company produces 6 units of A and 9 units of B the value of the objective function is equal to

A)$36.
B)$81.
C)$108.
D)$117.

Question 30

The area that contains the values that satisfies all the constraints in a linear programming problem is known as the _________________ space.

A)optimal solution
B)non-optimal solution
C)feasible solution
D)infeasible solution.

Question 31

If a resource has positive shadow price,its slack is __________.

A)larger than or equal to zero
B)positive
C)zero
D)There is not enough information to answer the question.

Question 32

TicToc produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $3000 and a maximum of 1000 hours of labor per week.Each A produced generates $35.00 in profit for the company.Each B produced generates $25.00 in profit for the company.If the company produces 100 units of A and 200 units of B the value of the objective function is equal to

A)$2,800.
B)$8,500.
C)$9,500.
D)$11,800.

Question 33

How is linear programming useful to an operations manager?

Question 34

What is meant by the term "shadow price" in linear programming?

Question 35

The simplex method is a solution method used for linear programming problems that have

A)no constraints.
B)at least one constraint.
C)at least two constraints.
D)at least three constraints.

Question 36

If a resource has positive slack,then its shadow price is __________.

A)larger than or equal to zero
B)positive
C)zero
D)There is not enough information to answer the question.

Question 37

TicToc produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $3000 and a maximum of 1000 hours of labor per week.Each A produced generates $35.00 in profit for the company.Each B produced generates $25.00 in profit for the company.The capacity constraint for labor is

A)12A + 8B > 1000.
B)12A + 8B < 1000.
C)4A + 3B < 1000.
D)4A + 3B > 1000.

Question 38

The optimal solution for a linear programming problem will always occur

A)when the slack price equals the surplus price.
B)when the surplus price equals the slack price.
C)at an extreme point.
D)at a non-extreme point.