Question 1

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 2

The amount that the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the

Accepted Answer

A) dual price. 
B) surplus variable. 
C) reduced cost. 
D) upper limit. 
A) dual price. 
B) surplus variable. 
C) reduced cost. 
D) upper limit. C

Question 3

The dual price for a percentage constraint provides a direct answer to questions about the effect of increases or decreases in that percentage.

Accepted Answer

A) True 
 B)False  False

Question 4

For any constraint, either its slack/surplus value must be zero or its dual price must be zero.

Accepted Answer

A) True 
 B)False

Question 5

The 100% Rule does not imply that the optimal solution will necessarily change if the percentage exceeds 100%.

Accepted Answer

A) True 
 B)False

Question 6

For a minimization problem, a positive dual price indicates the value of the objective function will increase.

Accepted Answer

A) True 
 B)False

Question 7

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

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 8

There is a dual price for every decision variable in a model.

Accepted Answer

A) True 
 B)False

Question 9

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

Question 10

Sensitivity analysis information in computer output is based on the assumption of

Accepted Answer

A) no coefficient change. 
B) one coefficient change. 
C) two coefficient change. 
D) all coefficients change. 
A) no coefficient change. 
B) one coefficient change. 
C) two coefficient change. 
D) all coefficients change.

Question 11

The reduced cost for a positive decision variable is 0.

Accepted Answer

A) True 
 B)False

Question 12

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 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 amount by which an objective function coefficient would have to improve before it would be possible for the corresponding variable to assume a positive value in the optimal solution is called the

Accepted Answer

A) reduced cost. 
B) relevant cost. 
C) sunk cost. 
D) dual price. 
A) reduced cost. 
B) relevant cost. 
C) sunk cost. 
D) dual price.

Question 15

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 the above is 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 the above is true.

Question 16

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 17

The amount of a sunk cost will vary depending on the values of the decision variables.

Accepted Answer

A) True 
 B)False

Question 18

An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost.The correct interpretation of the dual price associated with the labor hours constraint is

Accepted Answer

A) the maximum premium (say for overtime) over the normal price that the company would be willing to pay. 
B) the upper limit on the total hourly wage the company would pay. 
C) the reduction in hours that could be sustained before the solution would change. 
D) the number of hours by which the right-hand side can change before there is a change in the solution point. 
A) the maximum premium (say for overtime) over the normal price that the company would be willing to pay. 
B) the upper limit on the total hourly wage the company would pay. 
C) the reduction in hours that could be sustained before the solution would change. 
D) the number of hours by which the right-hand side can change before there is a change in the solution point.

Question 19

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 20

A constraint with a positive slack value

Accepted Answer

A) will have a positive dual price. 
B) will have a negative dual price. 
C) will have a dual price of zero. 
D) has no restrictions for its dual price. 
A) will have a positive dual price. 
B) will have a negative dual price. 
C) will have a dual price of zero. 
D) has no restrictions for its dual price.

Exam 3: LP Sensitivity Analysis and Interpretation of Solution

The 100% Rule compares

The amount that the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the

The dual price for a percentage constraint provides a direct answer to questions about the effect of increases or decreases in that percentage.

For any constraint, either its slack/surplus value must be zero or its dual price must be zero.

The 100% Rule does not imply that the optimal solution will necessarily change if the percentage exceeds 100%.

For a minimization problem, a positive dual price indicates the value of the objective function will increase.

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

There is a dual price for every decision variable in a model.

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.

Sensitivity analysis information in computer output is based on the assumption of

The reduced cost for a positive decision variable is 0.

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

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

The amount by which an objective function coefficient would have to improve before it would be possible for the corresponding variable to assume a positive value in the optimal solution is called the

The range of feasibility measures

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

The amount of a sunk cost will vary depending on the values of the decision variables.

An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost.The correct interpretation of the dual price associated with the labor hours constraint is

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?

A constraint with a positive slack value

Introduction

Introduction to Linear Programming

Linear Programming Applications

Advanced Linear Programming Applications

Distribution and Network Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

LP: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

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