Question $56(3$ points$)$

You are the production manager for a gear manufacturer. The following report presents the result of a linear program to determine the optimal product mix between four possible products $($Gears A$,$ B$,$ C$,$ and D$),$ which would use the following resources: drilling hours, milling hours, lathe hours, and inspection hours. The coefficients of the objective function represent the profit to be made from the manufacture of each type of gear.

Variable Cells

Cell

Name

Final Value

Reduced Cost

Objective Coefficient

Allowable Increase

Allowable Decrease

$C$$4$

Number to Make Gear A

$565\mathrm{.}4$

$0\mathrm{.}00$

$16$

$15\mathrm{.}20$

$3\mathrm{.}50$

$D$$4$

Number to Make Gear B

$0\mathrm{.}0$

$-1\mathrm{.}24$

$9$

$1\mathrm{.}24$

$1$E$+30$

$E$$4$

Number to Make Gear C

$1052\mathrm{.}9$

$0\mathrm{.}00$

$13$

$5\mathrm{.}00$

$3\mathrm{.}50$

$F$$4$

Number to Make Gear D

$0\mathrm{.}0$

$-3\mathrm{.}94$

$8$

$3\mathrm{.}94$

$1$E$+30$

Constraints

Cell

Name

Final Value

Shadow Price

Constraint

R$.$H$.$ Side

Allowable

Increase

Allowable

Decrease

G$$8$

Drilling Hours

$700\mathrm{.}0$

$22\mathrm{.}4$

$700$

$3\mathrm{.}36$

$298\mathrm{.}33$

$G$$9$

Milling Hours

$886\mathrm{.}8$

$0\mathrm{.}0$

$890$

$1$E$+30$

$3\mathrm{.}21$

$G$$10$

Lathe Hours

$1205\mathrm{.}0$

$5\mathrm{.}9$

$1205$

$17\mathrm{.}58$

$427\mathrm{.}22$

$G$$11$

Inspection Hours

$404\mathrm{.}6$

$0\mathrm{.}0$

$525$

$1$E$+30$

$120\mathrm{.}40$

What are the potential effects on the production process if additional milling hours become available.

Question $56$ options:

Additional milling hours will decrease the total profit

Additional milling hours will significantly increase total profit

Additional milling hours will decrease the total profit as the shadow price is $$0\mathrm{.}00$

Additional milling hours will have no effect on total profit