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.

---

Definitions:

Gonorrhea

A sexually transmitted bacterial infection that is often asymptomatic but can cause serious reproductive complications.

Hypodermic Needles

Thin, hollow needles used for injecting substances into the body or extracting fluids, commonly associated with medical applications.

Exercise

Physical activities undertaken to maintain or improve health and fitness, often consisting of various forms of physical training, sports, or activities.

Stress Level

The intensity of stress, reflecting the extent to which environmental demands strain an individual's coping capacity.