Deck 14: Operational Decision-Making Tools: Linear Programming

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

Linear programming is a mathematical modeling technique based on linear relationships

Question 9

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 10

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

Question 11

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.

Question 12

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 13

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 14

The constraints in a linear programming formulation define the feasible solution space.

Question 15

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

Question 16

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

Question 17

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

Question 18

Most real-world linear programming problems are solved graphically.

Question 19

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

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

Question 20

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

Question 21

How is linear programming useful to an operations manager?

Question 22

A company 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 capacity constraint for Process 2 is

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

Question 23

A company 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 24

A company 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 constraint for process 1 is represented by

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

Question 25

A company 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 company's objective function is

A)$6.00A + $9.00B
B)$9.00A + $6.00B
C)$6.00A - $9.00B
D)$6.00A*$9.00B

Question 26

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

Question 27

Briefly define the components that comprise a linear programming model.

Question 28

A company 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 29

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.