Variable cells $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Reduced } \\ \text { Cost } \end{array} & \begin{array}{c} \text { Objective } \\ \text { Coefficient } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{B} \$ 6 & \text { Activity 1 } & 0 & 425 & 500 & 1 \mathrm{E}+30 & 425 \\ \hline \$ \mathrm{C} \$ 6 & \text { Activity 2 } & 27.5 & 0.0 & 300 & 500 & 300 \\ \hline \$ \mathrm{D} \$ & \text { Activity 3 } & 0 & 250 & 400 & 1 \mathrm{E}+30 & 250 \\ \hline \end{array}$ Constraints $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Shadow } \\ \text { Price } \end{array} & \begin{array}{c} \text { Constraint } \\ \text { R.H. Side } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{E} \$ 2 & \text { Benefit A } & 110 & 0 & 60 & 50 & 1 \mathrm{E}+3 \mathrm{C} \\ \hline \$ \mathrm{E} \$ 3 & \text { Benefit B } & 110 & 75 & 110 & 1 \mathrm{E}+30 & 46 \\ \hline \$\mathrm{E} \$ 4 & \text { Benefit C } & 137.5 & 0 & 80 & 57.5 & 1 \mathrm{E}+30 \\ \hline \end{array}$ If the coefficient for Activity 1 in the objective function changes to $50, then the objective function value:

A) will decrease by $450. B) is $0. C) will decrease by $2750. D) will remain the same. E) can only be discovered by resolving the problem. A) will decrease by $450. B) is $0. C) will decrease by $2750. D) will remain the same. E) can only be discovered by resolving the problem. E

Variable cells \[\begin{array} { | r | r | r | r | r | r | r | } \hline \text { Cell } & \text { Name } & \begin{array} { c } \text { Final } \\ \text { Value } \end{array} & \begin{array} { c } \text { Reduced } \\ \text { Cost } \end{array} & \begin{array} { c } \text { Objective } \\ \text { Codficient } \end{array} & \begin{array} { c } \text { Allowable } \\ \text { Increase } \end{array} & \begin{array} { c } \text { Allowuble } \\ \text { Decrease } \end{array} \\ \hline \text { \$B\$6 } & \text { Activity 1 } & 3 & 0 & 30 & 23 & 17 \\ \hline \text { \$C\$6 } & \text { Activity 2 } & 6 & 0 & 40 & 50 & 10 \\ \hline \text { \$D\$6 } & \text { Activity 3 } & 0 & - 7 & 20 & 7 & 1 \mathrm { E } + 30 \\ \hline \end{array}\] Constraints $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Shadow } \\ \text { Price } \end{array} & \begin{array}{c} \text { Constraint } \\ \text { R.H. Side } \end{array} & {\begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array}} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{E} \$ 2 & \text { Resource A } & 20 & 7.78 & 20 & 10 & 12.5 \\ \hline \$ \mathrm{E} \$ 3 & \text { Resource B } & 30 & 6 & 30 & 50 & 10 \\ \hline \$ \mathrm{E} \$ 4 & \text { Resource C } & 18 & \mathrm{0} & 40 & 1 \mathrm{E}+30 & 22\\ \hline \end{array}$ If the right-hand side of Resource B is increased by 30, and the right-hand side of Resource C is decreased by 10, then:

A) the optimal solution remains the same. B) the optimal solution will change. C) the shadow prices are valid. D) the shadow prices may or may not be valid. E) None of the choices is correct. A) the optimal solution remains the same. B) the optimal solution will change. C) the shadow prices are valid. D) the shadow prices may or may not be valid. E) None of the choices is correct.

Variable cells $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Reduced } \\ \text { Cost } \end{array} & \begin{array}{c} \text { Objective } \\ \text { Coefficient } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{B} \$ 6 & \text { Activity 1 } & 0 & 425 & 500 & 1 \mathrm{E}+30 & 425 \\ \hline \$ \mathrm{C} \$ 6 & \text { Activity 2 } & 27.5 & 0.0 & 300 & 500 & 300 \\ \hline \$ \mathrm{D} \$ & \text { Activity 3 } & 0 & 250 & 400 & 1 \mathrm{E}+30 & 250 \\ \hline \end{array}$ Constraints $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Shadow } \\ \text { Price } \end{array} & \begin{array}{c} \text { Constraint } \\ \text { R.H. Side } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{E} \$ 2 & \text { Benefit A } & 110 & 0 & 60 & 50 & 1 \mathrm{E}+3 \mathrm{C} \\ \hline \$ \mathrm{E} \$ 3 & \text { Benefit B } & 110 & 75 & 110 & 1 \mathrm{E}+30 & 46 \\ \hline \$\mathrm{E} \$ 4 & \text { Benefit C } & 137.5 & 0 & 80 & 57.5 & 1 \mathrm{E}+30 \\ \hline \end{array}$ If the right-hand side of Resource B changes to 80, then the objective function value:

A) will decrease by $750. B) will decrease by $1,500. C) will decrease by $2,250. D) will remain the same. E) can only be discovered by resolving the problem. A) will decrease by $750. B) will decrease by $1,500. C) will decrease by $2,250. D) will remain the same. E) can only be discovered by resolving the problem.

variable cells \[\begin{array} { | r | r | r | r | r | r | r | } \hline \text { Cell } & \text { Name } & \begin{array} { c } \text { Final } \\ \text { Value } \end{array} & \begin{array} { c } \text { Reduced } \\ \text { Cost } \end{array} & \begin{array} { c } \text { Objective } \\ \text { Codficient } \end{array} & \begin{array} { c } \text { Allowable } \\ \text { Increase } \end{array} & \begin{array} { c } \text { Allowuble } \\ \text { Decrease } \end{array} \\ \hline \text { \$B\$6 } & \text { Activity 1 } & 3 & 0 & 30 & 23 & 17 \\ \hline \text { \$C\$6 } & \text { Activity 2 } & 6 & 0 & 40 & 50 & 10 \\ \hline \text { \$D\$6 } & \text { Activity 3 } & 0 & - 7 & 20 & 7 & 1 \mathrm { E } + 30 \\ \hline \end{array}\] Constraints $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Shadow } \\ \text { Price } \end{array} & \begin{array}{c} \text { Constraint } \\ \text { R.H. Side } \end{array} & {\begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array}} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{E} \$ 2 & \text { Resource A } & 20 & 7.78 & 20 & 10 & 12.5 \\ \hline \$ \mathrm{E} \$ 3 & \text { Resource B } & 30 & 6 & 30 & 50 & 10 \\ \hline \$ \mathrm{E} \$ 4 & \text { Resource C } & 18 & \mathrm{0} & 40 & 1 \mathrm{E}+30 & 22\\ \hline \end{array}$ What is the optimal objective function value for this problem?

A) It cannot be determined from the given information. B) $7.78 C) $240 D) $90 E) $330 A) It cannot be determined from the given information. B) $7.78 C) $240 D) $90 E) $330

Variable cells $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Reduced } \\ \text { Cost } \end{array} & \begin{array}{c} \text { Objective } \\ \text { Coefficient } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{B} \$ 6 & \text { Activity 1 } & 0 & 425 & 500 & 1 \mathrm{E}+30 & 425 \\ \hline \$ \mathrm{C} \$ 6 & \text { Activity 2 } & 27.5 & 0.0 & 300 & 500 & 300 \\ \hline \$ \mathrm{D} \$ & \text { Activity 3 } & 0 & 250 & 400 & 1 \mathrm{E}+30 & 250 \\ \hline \end{array}$ Constraints $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Shadow } \\ \text { Price } \end{array} & \begin{array}{c} \text { Constraint } \\ \text { R.H. Side } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{E} \$ 2 & \text { Benefit A } & 110 & 0 & 60 & 50 & 1 \mathrm{E}+3 \mathrm{C} \\ \hline \$ \mathrm{E} \$ 3 & \text { Benefit B } & 110 & 75 & 110 & 1 \mathrm{E}+30 & 46 \\ \hline \$\mathrm{E} \$ 4 & \text { Benefit C } & 137.5 & 0 & 80 & 57.5 & 1 \mathrm{E}+30 \\ \hline \end{array}$ What is the allowable range for the objective function coefficient for Activity 3?

A) 150 ? A3 ? ? B) 0 ? A3 ? 650 C) 0 ? A3 ? 250 D) 400 ? A3 ? ? E) 300 ? A3 ? 500 A) 150 ? A3 ? ? B) 0 ? A3 ? 650 C) 0 ? A3 ? 250 D) 400 ? A3 ? ? E) 300 ? A3 ? 500

Variable cells $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Reduced } \\ \text { Cost } \end{array} & \begin{array}{c} \text { Objective } \\ \text { Coefficient } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{B} \$ 6 & \text { Activity 1 } & 0 & 425 & 500 & 1 \mathrm{E}+30 & 425 \\ \hline \$ \mathrm{C} \$ 6 & \text { Activity 2 } & 27.5 & 0.0 & 300 & 500 & 300 \\ \hline \$ \mathrm{D} \$ & \text { Activity 3 } & 0 & 250 & 400 & 1 \mathrm{E}+30 & 250 \\ \hline \end{array}$ Constraints $\begin{array}{|r|r|r|r|r|r|r|} \hline \text { Cell } & \text { Name } & \begin{array}{c} \text { Final } \\ \text { Value } \end{array} & \begin{array}{c} \text { Shadow } \\ \text { Price } \end{array} & \begin{array}{c} \text { Constraint } \\ \text { R.H. Side } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Increase } \end{array} & \begin{array}{c} \text { Allowable } \\ \text { Decrease } \end{array} \\ \hline \$ \mathrm{E} \$ 2 & \text { Benefit A } & 110 & 0 & 60 & 50 & 1 \mathrm{E}+3 \mathrm{C} \\ \hline \$ \mathrm{E} \$ 3 & \text { Benefit B } & 110 & 75 & 110 & 1 \mathrm{E}+30 & 46 \\ \hline \$\mathrm{E} \$ 4 & \text { Benefit C } & 137.5 & 0 & 80 & 57.5 & 1 \mathrm{E}+30 \\ \hline \end{array}$ What is the allowable range of the right-hand-side for Resource A?

A) -? ? RHSA ? 60 B) 0 ? RHSA ? 110 C) -? ? RHSA ? 110 D) 110 ? RHSA ? 1600 E) 0 ? RHSA ? 160 A) -? ? RHSA ? 60 B) 0 ? RHSA ? 110 C) -? ? RHSA ? 110 D) 110 ? RHSA ? 1600 E) 0 ? RHSA ? 160

Exam 5: What-If Analysis for Linear Programming

Variable cells Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease \ \ 6 Activity 1 0 425 500 1+30 425 \ \ 6 Activity 2 27.5 0.0 300 500 300 \ \ Activity 3 0 250 400 1+30 250 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease \ \ 2 Benefit A 110 0 60 50 1+3 \ \ 3 Benefit B 110 75 110 1+30 46 mathrm E \ 4 Benefit C 137.5 0 80 57.5 1+30 If the coefficient for Activity 1 in the objective function changes to $50, then the objective function value:

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(Multiple Choice)

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Question 1

Correct Answer:

Verified

E

When certain parameters of a model represent managerial policy decisions, what-if analysis provides information about what the impact would be of altering these policy decisions.

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(True/False)

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Question 2

Correct Answer:

Verified

True

Which of the following are benefits of what-if analysis?

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(Multiple Choice)

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Question 3

Correct Answer:

Verified

A

One approach to robust optimization is to modify the original optimization problem by

(Multiple Choice)

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Question 4

Variable cells Cell Name Final Value Reduced Cost Objective Codficient Allowable Increase Allowuble Decrease \B \6 Activity 1 3 0 30 23 17 \C \6 Activity 2 6 0 40 50 10 \D \6 Activity 3 0 -7 20 7 1+30 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease \ \ 2 Resource A 20 7.78 20 10 12.5 \ \ 3 Resource B 30 6 30 50 10 \ \ 4 Resource C 18 40 1+30 22 If the right-hand side of Resource B is increased by 30, and the right-hand side of Resource C is decreased by 10, then:

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Question 5

A shadow price tells how much a decision variable can be increased or decreased without changing the value of the solution.

(True/False)

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Question 6

The allowable range gives ranges of values for the objective function coefficients within which the values of the decision variables are optimal.

(True/False)

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Question 7

Variable cells Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease \ \ 6 Activity 1 0 425 500 1+30 425 \ \ 6 Activity 2 27.5 0.0 300 500 300 \ \ Activity 3 0 250 400 1+30 250 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease \ \ 2 Benefit A 110 0 60 50 1+3 \ \ 3 Benefit B 110 75 110 1+30 46 mathrm E \ 4 Benefit C 137.5 0 80 57.5 1+30 If the right-hand side of Resource B changes to 80, then the objective function value:

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Question 8

If a change is made in only one of the objective function coefficients:

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Question 9

The term "allowable range for the right-hand-side" refers to coefficients of the objective function.

(True/False)

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Question 10

variable cells Cell Name Final Value Reduced Cost Objective Codficient Allowable Increase Allowuble Decrease \B \6 Activity 1 3 0 30 23 17 \C \6 Activity 2 6 0 40 50 10 \D \6 Activity 3 0 -7 20 7 1+30 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease \ \ 2 Resource A 20 7.78 20 10 12.5 \ \ 3 Resource B 30 6 30 50 10 \ \ 4 Resource C 18 40 1+30 22 What is the optimal objective function value for this problem?

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Question 11

When maximizing profit in a linear programming problem, the allowable increase and allowable decrease columns in the sensitivity report make it possible to find the range over which the profitability does not change.

(True/False)

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Question 12

The allowable range for an objective function coefficient indicates

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Question 13

In robust optimization, what is meant by the term "hard constraint"?

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Question 14

If the right-hand side value of a constraint in a two variable linear programming problems is changed, then:

(Multiple Choice)

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Question 15

What-if analysis can: I. be done graphically for problems with two decision variables. II. reduce a manager's confidence in the model that has been formulated. III. increase a manager's confidence in the model that has been formulated.

(Multiple Choice)

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Question 16

When a change in the value of an objective function coefficient remains within the allowable range, the optimal solution will also remain the same.

(True/False)

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Question 17

Every change in the value of an objective function coefficient will lead to a changed optimal solution.

(True/False)

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Question 18

Variable cells Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease \ \ 6 Activity 1 0 425 500 1+30 425 \ \ 6 Activity 2 27.5 0.0 300 500 300 \ \ Activity 3 0 250 400 1+30 250 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease \ \ 2 Benefit A 110 0 60 50 1+3 \ \ 3 Benefit B 110 75 110 1+30 46 mathrm E \ 4 Benefit C 137.5 0 80 57.5 1+30 What is the allowable range for the objective function coefficient for Activity 3?

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Question 19

Variable cells Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease \ \ 6 Activity 1 0 425 500 1+30 425 \ \ 6 Activity 2 27.5 0.0 300 500 300 \ \ Activity 3 0 250 400 1+30 250 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease \ \ 2 Benefit A 110 0 60 50 1+3 \ \ 3 Benefit B 110 75 110 1+30 46 mathrm E \ 4 Benefit C 137.5 0 80 57.5 1+30 What is the allowable range of the right-hand-side for Resource A?

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Question 20

When certain parameters of a model represent managerial policy decisions, what-if analysis provides information about what the impact would be of altering these policy decisions.

Which of the following are benefits of what-if analysis?

One approach to robust optimization is to modify the original optimization problem by

A shadow price tells how much a decision variable can be increased or decreased without changing the value of the solution.

The allowable range gives ranges of values for the objective function coefficients within which the values of the decision variables are optimal.

If a change is made in only one of the objective function coefficients:

The term "allowable range for the right-hand-side" refers to coefficients of the objective function.

When maximizing profit in a linear programming problem, the allowable increase and allowable decrease columns in the sensitivity report make it possible to find the range over which the profitability does not change.

The allowable range for an objective function coefficient indicates

In robust optimization, what is meant by the term "hard constraint"?

If the right-hand side value of a constraint in a two variable linear programming problems is changed, then:

What-if analysis can: I. be done graphically for problems with two decision variables. II. reduce a manager's confidence in the model that has been formulated. III. increase a manager's confidence in the model that has been formulated.

When a change in the value of an objective function coefficient remains within the allowable range, the optimal solution will also remain the same.

Every change in the value of an objective function coefficient will lead to a changed optimal solution.

Introduction

Linear Programming: Basic Concepts

Linear Programming: Formulation and Applications

The Art of Modeling With Spreadsheets

Network Optimization Problems

Using Binary Integer Programming to Deal With Yes-Or-No Decisions

Nonlinear Programming

Decision Analysis

Forecasting

Queueing Models

Computer Simulation: Basic Concepts

Computer Simulation With Analytic Solver

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