Question 1

It is usually quite easy to find the needed data for a linear programming study.

Accepted Answer

A) True 
 B)False

Question 2

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 A changes to 10, then the objective function value:

Accepted Answer

A)  will decrease by $12.50. 
B)  will decrease by $125. 
C)  will decrease by $77.80. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem. 
A)  will decrease by $12.50. 
B)  will decrease by $125. 
C)  will decrease by $77.80. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem.

Question 3

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.

Accepted Answer

A) True 
 B)False

Question 4

If the change to a right-hand side is within the allowable range, the value of the shadow price remains valid.

Accepted Answer

A) True 
 B)False

Question 5

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 coefficient for Activity 3 in the objective function changes to $30, then the objective function value:

Accepted Answer

A)  will increase by $70. 
B)  is $0. 
C)  will increase by $30. 
D)  will remain the same. 
E)  will increase by an unknown amount. 
A)  will increase by $70. 
B)  is $0. 
C)  will increase by $30. 
D)  will remain the same. 
E)  will increase by an unknown amount.

Question 6

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 coefficient for Activity 1 in the objective function changes to $40, then the objective function value:

Accepted Answer

A)  will increase by $77.80. 
B)  will increase by $23. 
C)  will increase by $30. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem. 
A)  will increase by $77.80. 
B)  will increase by $23. 
C)  will increase by $30. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem.

Question 7

If the change to a right-hand side is within the allowable range, the solution will remain the same.

Accepted Answer

A) True 
 B)False

Question 8

The purpose of a linear programming study is to help guide management's final decision by providing insights.

Accepted Answer

A) True 
 B)False

Question 9

According to the 100% rule for simultaneous changes in objective function coefficients, if the sum of the percentage changes exceeds 100%, the optimal solution definitely will change.

Accepted Answer

A) True 
 B)False

Question 10

A parameter analysis report can only be used to investigate changes in a single data cell at a time.

Accepted Answer

A) True 
 B)False

Question 11

What-if analysis:

Accepted Answer

A)  may involve changes in the objective function coefficients. 
B)  requires that only one parameter change while the rest are held fixed. 
C)  may involve changes in the right-hand side values. 
D)  All of the choices are correct. 
E)  None of the choices is correct. 
A)  may involve changes in the objective function coefficients. 
B)  requires that only one parameter change while the rest are held fixed. 
C)  may involve changes in the right-hand side values. 
D)  All of the choices are correct. 
E)  None of the choices is correct.

Question 12

A parameter analysis report can be used to investigate the changes in how many data cells at a time?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  All of the these. 
E)  1 or 2. 
A)  1 
B)  2 
C)  3 
D)  All of the these. 
E)  1 or 2.

Question 13

A parameter analysis report re-solves the problem for a range of values of a data cell.

Accepted Answer

A) True 
 B)False

Question 14

Whenever proportional changes are made to all the unit profits in a problem, the optimal solution will remain the same.

Accepted Answer

A) True 
 B)False

Question 15

Shadow price analysis is widely used to help management find the best trade-off between costs and benefits for a problem.

Accepted Answer

A) True 
 B)False

Question 16

When conducting robust optimization
I. The right-hand side of each ≤ constraint should be replaced with the minimum value.
II. The right-hand side of each ≤ constraint should be replaced with the maximum value.
III. The right-hand side of each ≥ constraint should be replaced with the maximum value.

Accepted Answer

A)  I only 
B)  II only 
C)  III only 
D)  I and III only 
E)  II and III only 
A)  I only 
B)  II only 
C)  III only 
D)  I and III only 
E)  II and III only

Question 17

In linear programming, what-if analysis is associated with determining the effect of changing:
I. objective function coefficients.
II. right-hand side values of constraints.
III. decision variable values.

Accepted Answer

A)  objective function coefficients and right-hand side values of constraints. 
B)  right-hand side values of constraints and decision variable values. 
C)  objective function coefficients, right-hand side values of constraints, and decision variable values. 
D)  objective function coefficients and decision variable values. 
E)  None of the choices is correct. 
A)  objective function coefficients and right-hand side values of constraints. 
B)  right-hand side values of constraints and decision variable values. 
C)  objective function coefficients, right-hand side values of constraints, and decision variable values. 
D)  objective function coefficients and decision variable values. 
E)  None of the choices is correct.

Question 18

If the sum of the percentage changes of the right-hand sides does not exceed 100%, then the solution will definitely remain optimal.

Accepted Answer

A) True 
 B)False

Question 19

Managerial decisions regarding right-hand sides are often interrelated and so frequently are considered simultaneously.

Accepted Answer

A) True 
 B)False

Question 20

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 C changes to 140, then the objective function value:

Accepted Answer

A)  will increase by $137.50. 
B)  will increase by $57.50. 
C)  will increase by $80. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem. 
A)  will increase by $137.50. 
B)  will increase by $57.50. 
C)  will increase by $80. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem.

It is usually quite easy to find the needed data for a linear programming study.

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.

If the change to a right-hand side is within the allowable range, the value of the shadow price remains valid.

If the change to a right-hand side is within the allowable range, the solution will remain the same.

The purpose of a linear programming study is to help guide management's final decision by providing insights.

According to the 100% rule for simultaneous changes in objective function coefficients, if the sum of the percentage changes exceeds 100%, the optimal solution definitely will change.

A parameter analysis report can only be used to investigate changes in a single data cell at a time.

What-if analysis:

A parameter analysis report can be used to investigate the changes in how many data cells at a time?

A parameter analysis report re-solves the problem for a range of values of a data cell.

Whenever proportional changes are made to all the unit profits in a problem, the optimal solution will remain the same.

Shadow price analysis is widely used to help management find the best trade-off between costs and benefits for a problem.

In linear programming, what-if analysis is associated with determining the effect of changing: I. objective function coefficients. II. right-hand side values of constraints. III. decision variable values.

If the sum of the percentage changes of the right-hand sides does not exceed 100%, then the solution will definitely remain optimal.

Managerial decisions regarding right-hand sides are often interrelated and so frequently are considered simultaneously.

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

Filters

Exam 5: What-If Analysis for Linear Programming

It is usually quite easy to find the needed data for a linear programming study.

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.

If the change to a right-hand side is within the allowable range, the value of the shadow price remains valid.

If the change to a right-hand side is within the allowable range, the solution will remain the same.

The purpose of a linear programming study is to help guide management's final decision by providing insights.

According to the 100% rule for simultaneous changes in objective function coefficients, if the sum of the percentage changes exceeds 100%, the optimal solution definitely will change.

A parameter analysis report can only be used to investigate changes in a single data cell at a time.

What-if analysis:

A parameter analysis report can be used to investigate the changes in how many data cells at a time?

A parameter analysis report re-solves the problem for a range of values of a data cell.

Whenever proportional changes are made to all the unit profits in a problem, the optimal solution will remain the same.

Shadow price analysis is widely used to help management find the best trade-off between costs and benefits for a problem.

In linear programming, what-if analysis is associated with determining the effect of changing: I. objective function coefficients. II. right-hand side values of constraints. III. decision variable values.

If the sum of the percentage changes of the right-hand sides does not exceed 100%, then the solution will definitely remain optimal.

Managerial decisions regarding right-hand sides are often interrelated and so frequently are considered simultaneously.

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

Filters