The production manager for the Whoppy soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). The company operates one 8-hour shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup, is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case.
The formulation for this problem is given below.
MAX Z = $3R + $2D
s.t.
&emsp; &emsp;2R + 4D ? 480
&emsp; &emsp;5R + 3D ? 675
The sensitivity report is given below.
Adjustable Cells
$\begin{array}{lcccccc}
\text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Reduced } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { Objective } \
\text { Coefficient }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{~B} \$ 6 && \text { Regular }=90.00 & 0.00 & 3 & 0.33 & 2 \
\hline \$ \mathrm{C} \$ 6 && \text { Diet }=75.00 & 0.00 & 2 & 4 & 0.2 \
\hline
\end{array}$ Constraints
$\begin{array}{ccccccc}
\text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Shadow } \
\text { Price }
\end{array} & \begin{array}{c}
\text { Constraint } \
\text { R.H. Side }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline
\$ \mathrm{E} \$ 3 & \text { Production (minutes) } & 480.00 & 0.07 & 480 & 420 & 210 \
\hline \$\text { E } \$ 4 & \text { Syrup (gallons) } & 675.00 & 0.57 & 675 & 525 & 315 \
\hline
\end{array}$
-What is the sensitivity range of the production time?

Question

The production manager for the Whoppy soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). The company operates one 8-hour shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup, is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case.
The formulation for this problem is given below.
MAX Z = $3R + $2D
s.t.
&emsp; &emsp;2R + 4D ? 480
&emsp; &emsp;5R + 3D ? 675
The sensitivity report is given below.
Adjustable Cells
 $\begin{array}{lcccccc}
\text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Reduced } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { Objective } \
\text { Coefficient }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{~B} \$ 6 && \text { Regular }=90.00 & 0.00 & 3 & 0.33 & 2 \
\hline \$ \mathrm{C} \$ 6 && \text { Diet }=75.00 & 0.00 & 2 & 4 & 0.2 \
\hline
\end{array}$ Constraints
 $\begin{array}{ccccccc}
\text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Shadow } \
\text { Price }
\end{array} & \begin{array}{c}
\text { Constraint } \
\text { R.H. Side }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline
\$ \mathrm{E} \$ 3 & \text { Production (minutes) } & 480.00 & 0.07 & 480 & 420 & 210 \
\hline \$\text { E } \$ 4 & \text { Syrup (gallons) } & 675.00 & 0.57 & 675 & 525 & 315 \
\hline
\end{array}$
-What is the sensitivity range of the production time?

Quizplus · Accepted Answer

The Answer of The production manager for the Whoppy soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). The company operates one 8-hour shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup, is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case.
The formulation for this problem is given below.
MAX Z = $3R + $2D
s.t.
&emsp; &emsp;2R + 4D ? 480
&emsp; &emsp;5R + 3D ? 675
The sensitivity report is given below.
Adjustable Cells
 $\begin{array}{lcccccc}
\text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Reduced } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { Objective } \
\text { Coefficient }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm{~B} \$ 6 && \text { Regular }=90.00 & 0.00 & 3 & 0.33 & 2 \
\hline \$ \mathrm{C} \$ 6 && \text { Diet }=75.00 & 0.00 & 2 & 4 & 0.2 \
\hline
\end{array}$ Constraints
 $\begin{array}{ccccccc}
\text { Cell } & \text { Name } & \begin{array}{c}
\text { Final } \
\text { Value }
\end{array} & \begin{array}{c}
\text { Shadow } \
\text { Price }
\end{array} & \begin{array}{c}
\text { Constraint } \
\text { R.H. Side }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array}{c}
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline
\$ \mathrm{E} \$ 3 & \text { Production (minutes) } & 480.00 & 0.07 & 480 & 420 & 210 \
\hline \$\text { E } \$ 4 & \text { Syrup (gallons) } & 675.00 & 0.57 & 675 & 525 & 315 \
\hline
\end{array}$
-What is the sensitivity range of the production time?

The Production Manager for the Whoppy Soft Drink Company Is