The Production Manager for the Whoppy Soft Drink Company Is

question 87

Short Answer

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.
   2R + 4D ? 480
   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 optimal daily profit?

---

Definitions:

Slope

The rate of change in the dependent variable for a unit change in the independent variable in a linear relationship.

Regression Line

A line of best fit through a scatterplot of data points in regression analysis, showing the relationship between the independent and dependent variables.

Positive

A term often used in statistics to denote a value or outcome that is above zero or indicates the presence of a condition or characteristic.

Least Squares

A mathematical approach used to approximate the solution of overdetermined systems, minimizing the sum of the squares of the differences between observed and estimated values.