Consider the Following Linear Program, Which Maximizes Profit for Two

question 8

Short Answer

Consider the following linear program, which maximizes profit for two products--regular (R) and super (S):
MAX 50R + 75S
s.t.
   1.2 R + 1.6 S ? 600 assembly (hours)
   0.8 R + 0.5 S ? 300 paint (hours)
.   16 R + 0.4 S ? 100 inspection (hours)
Sensitivity Report:
$\begin{array}{ccccccc}\text { Cell } & \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Reduced } \\\text { Cost }\end{array} & \begin{array}{c}\text { Objective } \\\text { Coefficient }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \$ \mathrm{~B} \$ 7 & \text { Regular }= & 291.67 & 0.00 & 50 & 70 & 20 \\\hline \text { \$C } \$ 7 & \text { Super }= & 133.33 & 0.00 & 75 & 50 & 43.75 \\\hline\end{array}$



$\begin{array}{llrccc}\text { Cell } \quad \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Shadow } \\\text { Price }\end{array} & \begin{array}{c}\text { Constraint } \\\text { R.H. Side }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \$ \mathrm{E} \$ 3 \text { Assembly (hr/unit) } & 563.33 & 0.0 \mathrm{C} & 600 & 1 \$\mathrm{E}+30 & 36.67 \\\hline \$\mathrm{E} \$ 4 \text { Paint (hr/unit) } & 300.00 & 33.33 & 300 & 39.29 & 175 \\\hline \$\mathrm{E} \$ 5 \text { Inspect (hr/unit) } & 100.00 & 145.83 & 100 & 12.94 & 40\end{array}$
-The profit on the super product could increase by ________ without affecting the product mix.

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Definitions:

Annual Profits

The total earnings of a business or company over the course of a year after all expenses have been deducted.

Complete Refund

The total return of money paid for a product or service, typically due to dissatisfaction or a defect.

External-operational Communication

The exchange of information between an organization and external parties, such as customers or vendors, that relates to its day-to-day operations.

Company Merger

The process by which two or more companies combine to form a single entity, often aiming to increase market share, reduce costs, or expand into new markets.