Consider the portion of the sensitivity analysis report that follows.Increasing the right-hand side constraint for $I$7 by 1 unit (240 to 241)will result in which of the following? $$\begin{array} { | l | l | l | l | l | l | l | }
\hline \text { Cell } & \text { Name } & \begin{array} { l }
\text { Final } \
\text { Value }
\end{array} & \begin{array} { l }
\text { Shadow } \
\text { Price }
\end{array} & \begin{array} { l }
\text { Constraint } \
R \mathrm { H } \text {. Side }
\end{array} & \begin{array} { l }
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array} { l }
\text { Alowable } \
\text { Decrease }
\end{array} \
\hline \$ 1 \$ 7 & \begin{array} { l }

Question

Consider the portion of the sensitivity analysis report that follows.Increasing the right-hand side constraint for $I$7 by 1 unit (240 to 241)will result in which of the following? $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Cell } & \text { Name } & \begin{array} { l } 
\text { Final } \
\text { Value }
\end{array} & \begin{array} { l } 
\text { Shadow } \
\text { Price }
\end{array} & \begin{array} { l } 
\text { Constraint } \
R \mathrm { H } \text {. Side }
\end{array} & \begin{array} { l } 
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array} { l } 
\text { Alowable } \
\text { Decrease }
\end{array} \
\hline \$ 1 \$ 7 & \begin{array} { l } 
< = \
\text { Usage }
\end{array} & 240 & 0.6 & 240 & 210 & 40 \
\hline \$ 1 \$ 8 & \begin{array} { l } 
< = \
\text { Usage }
\end{array} & 150 & 3.2 & 150 & 30 & 70 \
\hline
\end{array}$$
A)decrease the profit by $0.6
B)increase the profit by $3.2
C)increase the profit by $0.6.
D)decrease the profit by $0.6.

Quizplus · Accepted Answer

From the report, we see that increasing the RHS constraint for cell $I7$ by 1 unit (from 240 to 241) does not affect the shadow price for cell $I7$, but it increases the allowable increase to 210+1=211. This means we can increase the RHS value for cell $I7$ by up to 211-240= -29 (which means we reduce the RHS value) without affecting the optimal solution. Since this is a decrease in the RHS value, it would lead to a decrease in the profit. However, since the allowable decrease is larger than the allowable increase, we can conclude that the optimal solution is not very sensitive to changes in the RHS value for cell $I7$. Therefore, we can also infer that any small change in the RHS value will not change the optimal solution much. In particular, since the shadow price for cell $I7$ is positive, we can say that if we increase the RHS value for cell $I7$, it would increase the optimal profit by $0.6$ for every unit increase in the RHS value (up to the allowable increase of 211 units). Therefore, the correct answer choice is (C) "increase the profit by $0.6$".

Consider the Portion of the Sensitivity Analysis Report That Follows