Table $3\mathrm{.}1$: Regular & Super

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$)$

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

Sensitivity Report:

$\backslash$table$[[$Cell$,$Name,$\backslash$table$[[$Final$],[$Value$]],\backslash$table$[[$Reduced$],[$Cost$]],\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$$$B$$$,$Regular $=,291\mathrm{.}67,0\mathrm{.}00,50,70,20],[$$$C$$$7,$Super $=,133\mathrm{.}33,0\mathrm{.}00,75,50,43\mathrm{.}75]]$

$\backslash$table$[[$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$),100\mathrm{.}00,145\mathrm{.}83,100,12\mathrm{.}94,40]]$

If downtime reduced the available capacity for painting by $40$ hours $($from $300$ to $260$ hours$),$ profits would be reduced by $ $($round to the nearest dollar$).$