Regular & Super

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

MAX $50$R $+75$S

s$.$t$.$

$1\mathrm{.}2$ R $+1\mathrm{.}6$ S $<=600$ assembly $($hours$)$

$0\mathrm{.}8$ R $+0\mathrm{.}5$ S $<=300$ paint $($hours$)$

$\mathrm{.}16$ R $+0\mathrm{.}4$ S $<=100$ inspection $($hours$)$

Sensitivity Report:

Cell

Name

Final

Value

Reduced

Cost

Objective

Coefficient

Allowable

Increase

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

Final

Value

Shadow

Price

Constraint

R$.$H$.$ Side

Allowable

Increase

Allowable

Decrease

$E$$3$

Assembly $($hr$/$unit$)$

$563\mathrm{.}33$

$0\mathrm{.}00$

$600$

$1$E$+30$

$36\mathrm{.}67$

$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 optimal number of regular products to produce is $\_\_\_\_\_\_\_\_,$ and the optimal number of super products to produce is $\_\_\_\_\_\_\_\_,$ for total profits of $\_\_\_\_\_\_\_\_.$

Group of answer choices

$291\mathrm{.}67,133\mathrm{.}33,$ $$25,385$

$133\mathrm{.}33,291\mathrm{.}67,$ $$25,385$

$133\mathrm{.}33,291\mathrm{.}67,$ $$24,583$

$291\mathrm{.}67,133\mathrm{.}33,$ $$24,583$