Deck 19: Operational Decision-Making Tools: Linear Programming

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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 8

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 9

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

Question 10

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

Question 11

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

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

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

Question 14

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 15

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

Question 16

Linear programming is a mathematical modelling technique based on linear relationships.

Question 17

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

Question 18

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

Question 19

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 20

Most real-world linear programming problems are solved graphically.

Question 21

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 22

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 23

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

Question 24

Briefly define the components that comprise a linear programming model.

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 capacity constraint for Process 2 is

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

Question 26

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 27

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 28

How is linear programming useful to an operations manager?

Question 29

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.