Question $17$

$5$ pts

Consider the following linear program, which maximizes profit for two products $--$ regular $($R$)$ and super $(S)$ :

MAX $50R+75S$

s$.$t$.$

$1\mathrm{.}2R+1\mathrm{.}6S600$ assembly $($hours$)$

$0\mathrm{.}8R+0\mathrm{.}5S300$ paint $($hours$)$

$0\mathrm{.}16R+0\mathrm{.}4S100$ inspection $($hours$)$

The Sensitivity Report is as follows:

$\backslash$table$[[$Cell$,$Name,$\backslash$table$[[$Final$],[$Value$]],\backslash$table$[[$Reduced$],[$Cost$]],\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$$B$$7,$Regular $=,291\mathrm{.}67,0\mathrm{.}00,50,70,20],[$$$C$$$7,$Super $=,133\mathrm{.}33,0\mathrm{.}00,75,50,43\mathrm{.}75],[$Cell$,$Name,$\backslash$table$[[$Final$],[$Value$]],\backslash$table$[[$Shadow$],[$Price$]],\backslash$table$[[$Constraint$],[$R$.$H$.$ Side$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$$E$$3,$Assembly $($hr$/$unit$),563\mathrm{.}33,0\mathrm{.}00,600,1E+30,36\mathrm{.}67],[$$$E$$$4,$Paint $($hr$/$unit$),300\mathrm{.}00,33\mathrm{.}33,300,39\mathrm{.}29,175],[$$E$$5,$Inspect $($hr$/$unit$),100\mathrm{.}00,145\mathrm{.}83,100,12\mathrm{.}94,40]]$

The profit on the super product could increase by without affecting the product mix.