Question 1

When the cost of a resource is sunk, then the dual price can be interpreted as the

Accepted Answer

A)  minimum amount the firm should be willing to pay for one additional unit of the resource. 
B)  maximum amount the firm should be willing to pay for one additional unit of the resource. 
C)  minimum amount the firm should be willing to pay for multiple additional units of the resource. 
D)  maximum amount the firm should be willing to pay for multiple additional units of the resource. 
A)  minimum amount the firm should be willing to pay for one additional unit of the resource. 
B)  maximum amount the firm should be willing to pay for one additional unit of the resource. 
C)  minimum amount the firm should be willing to pay for multiple additional units of the resource. 
D)  maximum amount the firm should be willing to pay for multiple additional units of the resource. B

Question 2

Relevant costs should be reflected in the objective function, but sunk costs should not.

Accepted Answer

A) True 
 B)False  True

Question 3

The 100% Rule compares

Accepted Answer

A)  proposed changes to allowed changes. 
B)  new values to original values. 
C)  objective function changes to right-hand side changes. 
D)  dual prices to reduced costs. 
A)  proposed changes to allowed changes. 
B)  new values to original values. 
C)  objective function changes to right-hand side changes. 
D)  dual prices to reduced costs. A

Question 4

A section of output from The Management Scientist is shown here.   What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?

Accepted Answer

A)  Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same. 
B)  The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same. 
C)  The same decision variables will be positive, but their values, the objective function value, and the dual prices will change. 
D)  The problem will need to be resolved to find the new optimal solution and dual price. 
A)  Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same. 
B)  The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same. 
C)  The same decision variables will be positive, but their values, the objective function value, and the dual prices will change. 
D)  The problem will need to be resolved to find the new optimal solution and dual price.

Question 5

If the range of feasibility for b1 is between 16 and 37, then if b1 = 22 the optimal solution will not change from the original optimal solution.

Accepted Answer

A) True 
 B)False

Question 6

To solve a linear programming problem with thousands of variables and constraints

Accepted Answer

A)  a personal computer can be used. 
B)  a mainframe computer is required. 
C)  the problem must be partitioned into subparts. 
D)  unique software would need to be developed. 
A)  a personal computer can be used. 
B)  a mainframe computer is required. 
C)  the problem must be partitioned into subparts. 
D)  unique software would need to be developed.

Question 7

A negative dual price for a constraint in a minimization problem means

Accepted Answer

A)  as the right-hand side increases, the objective function value will increase. 
B)  as the right-hand side decreases, the objective function value will increase. 
C)  as the right-hand side increases, the objective function value will decrease. 
D)  as the right-hand side decreases, the objective function value will decrease. 
A)  as the right-hand side increases, the objective function value will increase. 
B)  as the right-hand side decreases, the objective function value will increase. 
C)  as the right-hand side increases, the objective function value will decrease. 
D)  as the right-hand side decreases, the objective function value will decrease.

Question 8

The range of feasibility measures

Accepted Answer

A)  the right-hand-side values for which the objective function value will not change. 
B)  the right-hand-side values for which the values of the decision variables will not change. 
C)  the right-hand-side values for which the dual prices will not change. 
D)  each of these choices are true. 
A)  the right-hand-side values for which the objective function value will not change. 
B)  the right-hand-side values for which the values of the decision variables will not change. 
C)  the right-hand-side values for which the dual prices will not change. 
D)  each of these choices are true.

Question 9

Which of the following is not a question answered by sensitivity analysis?

Accepted Answer

A)  If the right-hand side value of a constraint changes, will the objective function value change? 
B)  Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing? 
C)  By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility? 
D)  By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality? 
A)  If the right-hand side value of a constraint changes, will the objective function value change? 
B)  Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing? 
C)  By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility? 
D)  By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality?

Question 10

A section of output from The Management Scientist is shown here.   What will happen if the right-hand-side for constraint 2 increases by 200?

Accepted Answer

A)  Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same. 
B)  The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same. 
C)  The same decision variables will be positive, but their values, the objective function value, and the dual prices will change. 
D)  The problem will need to be resolved to find the new optimal solution and dual price. 
A)  Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same. 
B)  The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same. 
C)  The same decision variables will be positive, but their values, the objective function value, and the dual prices will change. 
D)  The problem will need to be resolved to find the new optimal solution and dual price.

Question 11

If the optimal value of a decision variable is zero and its reduced cost is zero, this indicates that alternative optimal solutions exist.

Accepted Answer

A) True 
 B)False

Question 12

The dual price measures, per unit increase in the right hand side of the constraint,

Accepted Answer

A)  the increase in the value of the optimal solution. 
B)  the decrease in the value of the optimal solution. 
C)  the improvement in the value of the optimal solution. 
D)  the change in the value of the optimal solution. 
A)  the increase in the value of the optimal solution. 
B)  the decrease in the value of the optimal solution. 
C)  the improvement in the value of the optimal solution. 
D)  the change in the value of the optimal solution.

Question 13

Decreasing the objective function coefficient of a variable to its lower limit will create a revised problem that is unbounded.

Accepted Answer

A) True 
 B)False

Question 14

The reduced cost for a positive decision variable is 0.

Accepted Answer

A) True 
 B)False

Question 15

Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.

Accepted Answer

A) True 
 B)False

Question 16

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

Accepted Answer

A)  optimal solution. 
B)  dual solution. 
C)  range of optimality. 
D)  range of feasibility. 
A)  optimal solution. 
B)  dual solution. 
C)  range of optimality. 
D)  range of feasibility.

Question 17

The dual value on the nonnegativitiy constraint for a variable is that variable's

Accepted Answer

A)  sunk cost. 
B)  surplus value. 
C)  reduced cost. 
D)  relevant cost. 
A)  sunk cost. 
B)  surplus value. 
C)  reduced cost. 
D)  relevant cost.

Question 18

If the dual price for the right-hand side of a $\le$ constraint is zero, there is no upper limit on its range of feasibility.

Accepted Answer

A) True 
 B)False

Question 19

Eight of the entries have been deleted from the LINDO output that follows. Use what you know about linear programming to find values for the blanks.
MIN 6 X1 + 7.5 X2 + 10 X3
SUBJECT TO
   END
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1) 612.50000
     NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:

Accepted Answer

It is easiest to calculate the values in

Question 20

If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.

Accepted Answer

A) True 
 B)False

When the cost of a resource is sunk, then the dual price can be interpreted as the

Relevant costs should be reflected in the objective function, but sunk costs should not.

The 100% Rule compares

A section of output from The Management Scientist is shown here. What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?

If the range of feasibility for b₁ is between 16 and 37, then if b₁ = 22 the optimal solution will not change from the original optimal solution.

To solve a linear programming problem with thousands of variables and constraints

A negative dual price for a constraint in a minimization problem means

The range of feasibility measures

Which of the following is not a question answered by sensitivity analysis?

A section of output from The Management Scientist is shown here. What will happen if the right-hand-side for constraint 2 increases by 200?

If the optimal value of a decision variable is zero and its reduced cost is zero, this indicates that alternative optimal solutions exist.

The dual price measures, per unit increase in the right hand side of the constraint,

Decreasing the objective function coefficient of a variable to its lower limit will create a revised problem that is unbounded.

The reduced cost for a positive decision variable is 0.

Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

The dual value on the nonnegativitiy constraint for a variable is that variable's

If the dual price for the right-hand side of a $\le$ constraint is zero, there is no upper limit on its range of feasibility.

If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.

Introduction

An Introduction to Linear Programming

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Filters

Exam 3: Linear Programming: Sensitivity Analysis and Interpretation of Solution

When the cost of a resource is sunk, then the dual price can be interpreted as the

Relevant costs should be reflected in the objective function, but sunk costs should not.

The 100% Rule compares

A section of output from The Management Scientist is shown here. What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?

If the range of feasibility for b1 is between 16 and 37, then if b1 = 22 the optimal solution will not change from the original optimal solution.

To solve a linear programming problem with thousands of variables and constraints

A negative dual price for a constraint in a minimization problem means

The range of feasibility measures

Which of the following is not a question answered by sensitivity analysis?

A section of output from The Management Scientist is shown here. What will happen if the right-hand-side for constraint 2 increases by 200?

If the optimal value of a decision variable is zero and its reduced cost is zero, this indicates that alternative optimal solutions exist.

The dual price measures, per unit increase in the right hand side of the constraint,

Decreasing the objective function coefficient of a variable to its lower limit will create a revised problem that is unbounded.

The reduced cost for a positive decision variable is 0.

Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

The dual value on the nonnegativitiy constraint for a variable is that variable's

If the dual price for the right-hand side of a ≤\le≤ constraint is zero, there is no upper limit on its range of feasibility.

If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.

Introduction

An Introduction to Linear Programming

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Filters

If the range of feasibility for b₁ is between 16 and 37, then if b₁ = 22 the optimal solution will not change from the original optimal solution.

If the dual price for the right-hand side of a $\le$ constraint is zero, there is no upper limit on its range of feasibility.