Question 1

Changing the objective function coefficients may or may not change the optimal solution, but it will always change the value of the objective function.

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
$\begin{array}{|r|r|r|r|r|r|r|}
\hline \text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Shadow } \
\text { Price }
\end{array} & \begin{array}{c}
\text { Constraint } \
\text { R.H. Side }
\end{array} & {\begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array}} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{E} \$ 2 & \text { Resource A } & 20 & 7.78 & 20 & 10 & 12.5 \
\hline \$ \mathrm{E} \$ 3 & \text { Resource B } & 30 & 6 & 30 & 50 & 10 \
\hline \$ \mathrm{E} \$ 4 & \text { Resource C } & 18 & \mathrm{0} & 40 & 1 \mathrm{E}+30 & 22\
\hline
\end{array}$
What is the allowable range for the right-hand-side for Resource C?

Accepted Answer

A)  18 ? RHSc ? ? 
B)  ? ? RHSc ? 62 
C)  ?2 ?RHSc ? ? 
D)  ? ? ? RHSc ? 40 
E)  0 ? RHSc ? 22 
A)  18 ? RHSc ? ? 
B)  ? ? RHSc ? 62 
C)  ?2 ?RHSc ? ? 
D)  ? ? ? RHSc ? 40 
E)  0 ? RHSc ? 22

Question 3

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?

Accepted Answer

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. 
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.

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
$\begin{array}{|r|r|r|r|r|r|r|}
\hline \text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Shadow } \
\text { Price }
\end{array} & \begin{array}{c}
\text { Constraint } \
\text { R.H. Side }
\end{array} & {\begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array}} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{E} \$ 2 & \text { Resource A } & 20 & 7.78 & 20 & 10 & 12.5 \
\hline \$ \mathrm{E} \$ 3 & \text { Resource B } & 30 & 6 & 30 & 50 & 10 \
\hline \$ \mathrm{E} \$ 4 & \text { Resource C } & 18 & \mathrm{0} & 40 & 1 \mathrm{E}+30 & 22\
\hline
\end{array}$
If the right-hand side of Resource B changes to 10, 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 5

The term "allowable range for an objective function coefficient" refers to a constraint's right-hand side quantity.

Accepted Answer

A) True 
 B)False

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
$\begin{array}{|r|r|r|r|r|r|r|}
\hline \text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Shadow } \
\text { Price }
\end{array} & \begin{array}{c}
\text { Constraint } \
\text { R.H. Side }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{E} \$ 2 & \text { Benefit A } & 110 & 0 & 60 & 50 & 1 \mathrm{E}+3 \mathrm{C} \
\hline \$ \mathrm{E} \$ 3 & \text { Benefit B } & 110 & 75 & 110 & 1 \mathrm{E}+30 & 46 \
\hline \$\mathrm{E} \$ 4 & \text { Benefit C } & 137.5 & 0 & 80 & 57.5 & 1 \mathrm{E}+30 \
\hline
\end{array}$
What is the optimal objective function value for this problem?

Accepted Answer

A)  It cannot be determined from the given information. 
B)  1,200 
C)  975 
D)  8,250 
E)  500 
A)  It cannot be determined from the given information. 
B)  1,200 
C)  975 
D)  8,250 
E)  500

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 right-hand side of Resource B changes to 10, then the objective function value:

Accepted Answer

A)  will decrease by $120. 
B)  will decrease by $60. 
C)  will decrease by $20. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem. 
A)  will decrease by $120. 
B)  will decrease by $60. 
C)  will decrease by $20. 
D)  will remain the same. 
E)  can only be discovered by resolving the problem.

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 coefficients of Activity 1 and Activity 2 in the objective function are both increased by $10, 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 9

Note: This question requires access to Solver.
In the following linear programming problem, what is the allowable increase in the right-hand side of the first constraint?
$\begin{array} { l l } 
\text { Maximize } P = 3 x + 15 y \
\text { subject to } & 2 x + 4 y \leq 12 \
& 5 x + 2 y \leq 10 \
\text { and } \quad x \geq 0 , y \geq 0
\end{array}$

Accepted Answer

A)  8 
B)  10 
C)  12 
D)  15 
E)  ? (infinity) 
A)  8 
B)  10 
C)  12 
D)  15 
E)  ? (infinity)

Question 10

Note: This question requires access to Solver.
In the following linear programming problem, what is the allowable increase for the objective function coefficient for variable x?
$\begin{array} { l l } 
\text { Maximize } P = 3 x + 15 y \
\text { subject to } & 2 x + 4 y \leq 12 \
& 5 x + 2 y \leq 10 \
\text { and } \quad x \geq 0 , y \geq 0
\end{array}$

Accepted Answer

A)  3 
B)  4.5 
C)  9 
D)  15 
E)  ? (infinity) 
A)  3 
B)  4.5 
C)  9 
D)  15 
E)  ? (infinity)

Question 11

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
$\begin{array}{|r|r|r|r|r|r|r|}
\hline \text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Shadow } \
\text { Price }
\end{array} & \begin{array}{c}
\text { Constraint } \
\text { R.H. Side }
\end{array} & {\begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array}} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{E} \$ 2 & \text { Resource A } & 20 & 7.78 & 20 & 10 & 12.5 \
\hline \$ \mathrm{E} \$ 3 & \text { Resource B } & 30 & 6 & 30 & 50 & 10 \
\hline \$ \mathrm{E} \$ 4 & \text { Resource C } & 18 & \mathrm{0} & 40 & 1 \mathrm{E}+30 & 22\
\hline
\end{array}$
Which parameter is most sensitive to an increase in its value?

Accepted Answer

A)  The objective coefficient of Activity 1. 
B)  The objective coefficient of Activity 2. 
C)  The objective coefficient of Activity 3. 
D)  All of the choices are correct. 
E)  None of the choices is correct. 
A)  The objective coefficient of Activity 1. 
B)  The objective coefficient of Activity 2. 
C)  The objective coefficient of Activity 3. 
D)  All of the choices are correct. 
E)  None of the choices is correct.

Question 12

A shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint.

Accepted Answer

A) True 
 B)False

Question 13

Resource B has right-hand side allowable decrease of 50. Resource C has right-hand side allowable decrease of 100. If the right-hand side of Resource B decreases by 30 and the right-hand side of Resource C decreases by 40, then

Accepted Answer

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

Question 14

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 B?
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)  Nothing 
B)  11.25 
C)  15 
D)  18.75 
E)  It is impossible to determine. 
A)  Nothing 
B)  11.25 
C)  15 
D)  18.75 
E)  It is impossible to determine.

Question 15

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 of Activity 1 in the objective function changes to $10, 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 above. 
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 above.

Question 16

Chance constraints are an available option in
I. Graphical linear programming.
II. The Solver tool included with Excel.
III. Analytic Solver.

Accepted Answer

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

Question 17

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?

Accepted Answer

A)  ?10 ? A2 ? 50 
B)  ?44 ? A2 ? 16 
C)  ?4 ? A2 ? 56 
D)  30 ? A2 ? 90 
E)  20 ? A2 ? 80 
A)  ?10 ? A2 ? 50 
B)  ?44 ? A2 ? 16 
C)  ?4 ? A2 ? 56 
D)  30 ? A2 ? 90 
E)  20 ? A2 ? 80

Question 18

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 130, 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 19

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

A) True 
 B)False

Question 20

When conducting robust optimization
I. Use the maximum value of each objective function coefficient for a maximization problem.
II. Use the minimum value of each objective function coefficient for a maximization problem.
III. Use the maximum value of each objective function coefficient for a minimization problem.

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

Changing the objective function coefficients may or may not change the optimal solution, but it will always change the value of the objective function.

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?

The term "allowable range for an objective function coefficient" refers to a constraint's right-hand side quantity.

Note: This question requires access to Solver. In the following linear programming problem, what is the allowable increase in the right-hand side of the first constraint? Maximize P=3x+15y subject to 2x+4y\leq12 5x+2y\leq10 and x\geq0,y\geq0

Note: This question requires access to Solver. In the following linear programming problem, what is the allowable increase for the objective function coefficient for variable x? Maximize P=3x+15y subject to 2x+4y\leq12 5x+2y\leq10 and x\geq0,y\geq0

A shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint.

Resource B has right-hand side allowable decrease of 50. Resource C has right-hand side allowable decrease of 100. If the right-hand side of Resource B decreases by 30 and the right-hand side of Resource C decreases by 40, then

Chance constraints are an available option in I. Graphical linear programming. II. The Solver tool included with Excel. III. Analytic Solver.

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.

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

Changing the objective function coefficients may or may not change the optimal solution, but it will always change the value of the objective function.

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?

The term "allowable range for an objective function coefficient" refers to a constraint's right-hand side quantity.

Note: This question requires access to Solver. In the following linear programming problem, what is the allowable increase in the right-hand side of the first constraint? Maximize P=3x+15y subject to 2x+4y\leq12 5x+2y\leq10 and x\geq0,y\geq0

Note: This question requires access to Solver. In the following linear programming problem, what is the allowable increase for the objective function coefficient for variable x? Maximize P=3x+15y subject to 2x+4y\leq12 5x+2y\leq10 and x\geq0,y\geq0

A shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint.

Resource B has right-hand side allowable decrease of 50. Resource C has right-hand side allowable decrease of 100. If the right-hand side of Resource B decreases by 30 and the right-hand side of Resource C decreases by 40, then

Chance constraints are an available option in I. Graphical linear programming. II. The Solver tool included with Excel. III. Analytic Solver.

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.

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