Question 1

A parameter analysis report can be used to easily investigate the changes in any number of data cells.

Accepted Answer

A) True 
 B)False

Question 2

Variable cells
$\begin{array}{|r|r|r|r|r|r|r|}
\hline \text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Reduced } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { Objective } \
\text { Coefficient }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{B} \$ 6 & \text { Activity 1 } & 0 & 425 & 500 & 1 \mathrm{E}+30 & 425 \
\hline \$ \mathrm{C} \$ 6 & \text { Activity 2 } & 27.5 & 0.0 & 300 & 500 & 300 \
\hline \$ \mathrm{D} \$ & \text { Activity 3 } & 0 & 250 & 400 & 1 \mathrm{E}+30 & 250 \
\hline
\end{array}$
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 objective coefficients of Activity 2 and Activity 3 are both decreased by $100, then:

Accepted Answer

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

Question 3

An optimal solution is only optimal with respect to a particular mathematical model that provides only a representation of the actual problem.

Accepted Answer

A) True 
 B)False

Question 4

A chance constraint
I. Replaces the right-hand side with the minimum value.
II. Allows the objective function coefficients to be replaced with random numbers.
III. Ensures that the chance constraint will never be violated.
IV. Can be used to model a soft constraint which can be violated at times.

Accepted Answer

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

Question 5

Variable cells
$\begin{array}{|r|r|r|r|r|r|r|}
\hline \text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Reduced } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { Objective } \
\text { Coefficient }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{B} \$ 6 & \text { Activity 1 } & 0 & 425 & 500 & 1 \mathrm{E}+30 & 425 \
\hline \$ \mathrm{C} \$ 6 & \text { Activity 2 } & 27.5 & 0.0 & 300 & 500 & 300 \
\hline \$ \mathrm{D} \$ & \text { Activity 3 } & 0 & 250 & 400 & 1 \mathrm{E}+30 & 250 \
\hline
\end{array}$
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 of Activity 2 in the objective function changes to $100, then:

Accepted Answer

A)  the original solution remains optimal. 
B)  the problem must be resolved to find the optimal solution. 
C)  the shadow price is valid. 
D)  the shadow price is not valid. 
E)  None of the choices is correct. 
A)  the original solution remains optimal. 
B)  the problem must be resolved to find the optimal solution. 
C)  the shadow price is valid. 
D)  the shadow price is not valid. 
E)  None of the choices is correct.

Question 6

Variable cells
$\begin{array}{|r|r|r|r|r|r|r|}
\hline \text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Reduced } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { Objective } \
\text { Coefficient }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{B} \$ 6 & \text { Activity 1 } & 0 & 425 & 500 & 1 \mathrm{E}+30 & 425 \
\hline \$ \mathrm{C} \$ 6 & \text { Activity 2 } & 27.5 & 0.0 & 300 & 500 & 300 \
\hline \$ \mathrm{D} \$ & \text { Activity 3 } & 0 & 250 & 400 & 1 \mathrm{E}+30 & 250 \
\hline
\end{array}$
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 is increased by 40, and the right-hand side of Resource B is decreased by 20, then:

Accepted Answer

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

Question 7

If the optimal solution will remain the same over a wide range of values for a particular coefficient in the objective function, then management will want to take special care to narrow this estimate down.

Accepted Answer

A) True 
 B)False

Question 8

To determine if an increase in an objective function coefficient will lead to a change in final values for decision variables, an analyst can do which of the following?
I. Compare the increase in the objective function coefficient to the allowable decrease.
II. Compare the increase in the objective function coefficient to the allowable increase.
III. Rerun the optimization to see if the final values change.

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 9

A shadow price reflects which of the following in a maximization problem?

Accepted Answer

A)  The marginal cost of adding additional resources. 
B)  The marginal gain in the objective value realized by adding one unit of a resource. 
C)  The marginal loss in the objective value realized by adding one unit of a resource. 
D)  The marginal gain in the objective value realized by subtracting one unit of a resource. 
E)  None of the choices is correct. 
A)  The marginal cost of adding additional resources. 
B)  The marginal gain in the objective value realized by adding one unit of a resource. 
C)  The marginal loss in the objective value realized by adding one unit of a resource. 
D)  The marginal gain in the objective value realized by subtracting one unit of a resource. 
E)  None of the choices is correct.

Question 10

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 2 in the objective function changes to $400, then the objective function value:

Accepted Answer

A)  will increase by $7,500. 
B)  will increase by $2,750. 
C)  will increase by $100. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem. 
A)  will increase by $7,500. 
B)  will increase by $2,750. 
C)  will increase by $100. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem.

Question 11

Activity 1 has an objective function coefficient allowable increase of 30. Activity 2 has an objective function coefficient allowable increase of 60. If both activities objective function coefficient increases by 20, what will happen to the final values in the optimal solution?

Accepted Answer

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

Question 12

Note: This question requires access to Solver.
In the following linear programming problem, how much would the firm be willing to pay for an additional 5 units of Resource A?
Maximize $P = 3 x + 15 y$
subject to $\quad 2 x + 4 y \leq 12$ (Resource A)
$5 x + 2 y \leq 10$ (Resource B)
and $\quad x \geq 0 , y \geq 0$.

Accepted Answer

A)  It is impossible to determine. 
B)  7.50 
C)  11.25 
D)  15 
E)  18.75 
A)  It is impossible to determine. 
B)  7.50 
C)  11.25 
D)  15 
E)  18.75

Question 13

The Solver report that shows the allowable ranges for objective function coefficients, allowable ranges for constraint right-hand sides, and shadow prices is called the

Accepted Answer

A)  Range report. 
B)  Sensitivity report. 
C)  Parameter report. 
D)  Solution report. 
E)  Answer report. 
A)  Range report. 
B)  Sensitivity report. 
C)  Parameter report. 
D)  Solution report. 
E)  Answer report.

Question 14

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

Accepted Answer

A)  A constraint that is not violated. 
B)  A constraint that has a shadow price of zero. 
C)  A constraint that can be violated slightly without serious repercussions. 
D)  A constraint that can be violated dramatically without serious repercussions. 
E)  A constraint that cannot be violated. 
A)  A constraint that is not violated. 
B)  A constraint that has a shadow price of zero. 
C)  A constraint that can be violated slightly without serious repercussions. 
D)  A constraint that can be violated dramatically without serious repercussions. 
E)  A constraint that cannot be violated.

Question 15

When even a small change in the value of a coefficient in the objective function can change the optimal solution, the coefficient is called:

Accepted Answer

A)  optimal. 
B)  sensitive. 
C)  out of the range. 
D)  within the range. 
E)  None of the choices is correct. 
A)  optimal. 
B)  sensitive. 
C)  out of the range. 
D)  within the range. 
E)  None of the choices is correct.

A parameter analysis report can be used to easily investigate the changes in any number of data cells.

An optimal solution is only optimal with respect to a particular mathematical model that provides only a representation of the actual problem.

A chance constraint I. Replaces the right-hand side with the minimum value. II. Allows the objective function coefficients to be replaced with random numbers. III. Ensures that the chance constraint will never be violated. IV. Can be used to model a soft constraint which can be violated at times.

If the optimal solution will remain the same over a wide range of values for a particular coefficient in the objective function, then management will want to take special care to narrow this estimate down.

A shadow price reflects which of the following in a maximization problem?

Activity 1 has an objective function coefficient allowable increase of 30. Activity 2 has an objective function coefficient allowable increase of 60. If both activities objective function coefficient increases by 20, what will happen to the final values in the optimal solution?

The Solver report that shows the allowable ranges for objective function coefficients, allowable ranges for constraint right-hand sides, and shadow prices is called the

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

When even a small change in the value of a coefficient in the objective function can change the optimal solution, the coefficient is called:

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

A parameter analysis report can be used to easily investigate the changes in any number of data cells.

An optimal solution is only optimal with respect to a particular mathematical model that provides only a representation of the actual problem.

A chance constraint I. Replaces the right-hand side with the minimum value. II. Allows the objective function coefficients to be replaced with random numbers. III. Ensures that the chance constraint will never be violated. IV. Can be used to model a soft constraint which can be violated at times.

If the optimal solution will remain the same over a wide range of values for a particular coefficient in the objective function, then management will want to take special care to narrow this estimate down.

A shadow price reflects which of the following in a maximization problem?

Activity 1 has an objective function coefficient allowable increase of 30. Activity 2 has an objective function coefficient allowable increase of 60. If both activities objective function coefficient increases by 20, what will happen to the final values in the optimal solution?

The Solver report that shows the allowable ranges for objective function coefficients, allowable ranges for constraint right-hand sides, and shadow prices is called the

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

When even a small change in the value of a coefficient in the objective function can change the optimal solution, the coefficient is called:

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