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Consider the Following Linear Program, Which Maximizes Profit for Two

Question 37

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:
 Cell  Name  Final  Value  Reduced  Cost  Objective  Coefficient  Allowable  Increase  Allowable  Decrease $ B$7 Regular =291.670.00507020 $C $7 Super =133.330.00755043.75\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}



 Cell  Name  Final  Value  Shadow  Price  Constraint  R.H. Side  Allowable  Increase  Allowable  Decrease $E$3 Assembly (hr/unit) 563.330.0C6001$E+3036.67$E$4 Paint (hr/unit) 300.0033.3330039.29175$E$5 Inspect (hr/unit) 100.00145.8310012.9440\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 optimal number of regular products to produce is ________, and the optimal number of super products to produce is ________, for total profits of ________.

Correct Answer:

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291.67, 13...

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