Question 1

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

Accepted Answer

Managerial decisions often involve complex relationships between right-hand sides, and thus they are often considered together.

Question 2

If a change is made in only one of the objective function coefficients:
A) the slope of the objective function line always will change.
B) the optimal solution always will change.
C) one or more of the decision variables always will change.
D) All of the choices are correct.
E) None of the choices is correct.

Accepted Answer

Changing one of the objective function coefficients alters the slope of the objective function line, but it does not necessarily change the optimal solution or the values of the decision variables.

Question 3

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.
A) I only.
B) II only.
C) III only.
D) All of the these.
E) I and III only.

Accepted Answer

The answer of What-if analysis can:
I. be done graphically for...

Question 4

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 allowable range for the right-hand-side for Resource C?
A) 18 ? RHSc ? ?
B) ? ? RHSc ? 62
C) ?2 ?RHSc ? ?
D) ? ? ? RHSc ? 40
E) 0 ? RHSc ? 22

Accepted Answer

The answer of Variable cells
\[\begin{array} { | r | r...

Question 5

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

Accepted Answer

The answer of A parameter analysis report can be used...

Question 6

In a problem with 4 decision variables, the 100% rule indicates that each objective coefficient can be safely increased by what amount without invalidating the current optimal solution?
A) 25%.
B) 25% of the allowable increase of that coefficient.
C) 100%.
D) 25% of the range of optimality.
E) It can't be determined from the information given.

Accepted Answer

The 100% rule states that the sum of the percentage changes in the objective coefficients, relative to their allowable increases or decreases, should not exceed 100% to maintain the current optimal solution.

Question 7

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:
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.

Accepted Answer

The answer of Variable cells
\[\begin{array} { | r | r...

Question 8

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:
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.

Accepted Answer

The answer of Variable cells
\[\begin{array} { | r | r...

Question 9

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

Accepted Answer

A parameter analysis report can investigate changes in multiple data cells at once by altering the parameters or variables of the analysis.

Question 10

variable cells
$$\begin{array} { | r | r | r | r | r | r | r | } 
\hline \text { Cell } & \text { Name } & \begin{array} { c } 
\text { Final } \
\text { Value }
\end{array} & \begin{array} { c } 
\text { Reduced } \
\text { Cost }
\end{array} & \begin{array} { c } 
\text { Objective } \
\text { Codficient }
\end{array} & \begin{array} { c } 
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array} { c } 
\text { Allowuble } \
\text { Decrease }
\end{array} \
\hline \text { \$B\$6 } & \text { Activity 1 } & 3 & 0 & 30 & 23 & 17 \
\hline \text { \$C\$6 } & \text { Activity 2 } & 6 & 0 & 40 & 50 & 10 \
\hline \text { \$D\$6 } & \text { Activity 3 } & 0 & - 7 & 20 & 7 & 1 \mathrm { E } + 30 \
\hline
\end{array}$$
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

Accepted Answer

The answer of variable cells
\[\begin{array} { | r | r...

Question 11

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

The statement refers to sensitivity analysis in linear programming. The optimality of a solution is not solely determined by the sum of the percentage changes of the right-hand sides being less than 100%. Other factors, such as changes in objective function coefficients and constraint coefficients, also affect optimality. The 100% rule provides a rough guideline but does not guarantee optimality under all circumstances.

Question 12

Which of the following are benefits of what-if analysis?
A) It pinpoints the sensitive parameters of the model.
B) It gives the new optimal solution if conditions change.
C) It tells management what policy decisions to make.
D) All of the choices are correct.
E) None of the choices is correct.

Accepted Answer

What-if analysis helps identify sensitive parameters by allowing users to see how changes in input variables affect outcomes.

Question 13

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.
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.

Accepted Answer

What-if analysis in linear programming involves examining how changes in the objective function coefficients and the right-hand side values of constraints affect the optimal solution. Changing decision variable values is not part of what-if analysis; instead, decision variable values are outcomes of the linear programming model.

Question 14

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 allowable range for the objective coefficient for Activity 2?
A) ?10 ? A2 ? 50
B) ?44 ? A2 ? 16
C) ?4 ? A2 ? 56
D) 30 ? A2 ? 90
E) 20 ? A2 ? 80

Accepted Answer

The answer of Variable cells
\[\begin{array} { | r | r...

Question 15

When a change occurs in the right-hand side values of one of the constraints, a proportional change will occur in one of the coefficients of the objective function.

Accepted Answer

Changing the right-hand side values of a constraint in a linear programming problem affects the feasible region and potentially the optimal solution, but it does not directly cause a proportional change in the coefficients of the objective function. These coefficients represent the contribution of each variable to the objective value and are independent of the constraint bounds.

Question 16

If the right-hand side value of a constraint in a two variable linear programming problems is changed, then:
A) the optimal measure of performance may change.
B) a parallel shift must be made in the graph of that constraint.
C) the optimal values for one or more of the decision variables may change.
D) All of the choices are correct.
E) None of the choices is correct.

Accepted Answer

Changing the right-hand side value of a constraint affects the feasible region and can lead to the optimal measure of performance changing. This can result in a parallel shift in the graph of that constraint and potentially a change in the optimal values for one or more decision variables. Therefore, all of the choices are correct.

Question 17

What-if analysis:
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.

Accepted Answer

What-if analysis can involve changes in objective function coefficients as well as right-hand side values. It also allows for changes in multiple parameters, as long as only one parameter is changed at a time while the rest are held fixed. Therefore, all of the choices are correct.

Question 18

When even a small change in the value of a coefficient in the objective function can change the optimal solution, the coefficient is called:
A) optimal.
B) sensitive.
C) out of the range.
D) within the range.
E) None of the choices is correct.

Accepted Answer

When even a small change in the value of a coefficient in the objective function can change the optimal solution, then the coefficient is said to be sensitive. This means that the solution is highly dependent on the value of the coefficient and any change in it can result in a different optimal solution. Therefore, option B is the correct choice.

Question 19

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

Accepted Answer

A shadow price reflects the marginal gain in the objective value realized by adding one unit of a resource. It measures the amount by which the objective function would improve if one additional unit of a particular resource were available.

Question 20

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

Accepted Answer

A parameter analysis report evaluates the impact of changing one or more parameters on a model, to determine how sensitive the model is to these changes, and to identify the best possible outcome within the given range of values for the parameter(s).

Quiz 5: What-If Analysis for Linear Programming

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

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

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.

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

In a problem with 4 decision variables, the 100% rule indicates that each objective coefficient can be safely increased by what amount without invalidating the current optimal solution?

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

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

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

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.

When a change occurs in the right-hand side values of one of the constraints, a proportional change will occur in one of the coefficients of the objective function.

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

What-if analysis:

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

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

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