Problem $2($Sensitivity Analysis$)$

DO NOT RE$-$SOLVE THIS PROBLEM IN EXCEL.$$ IT IS ALREADY SOLVED!$$ JUST ANSWER QUESTIONS $($a$),($b$),($c$),($d$),($e$)$ in this Word file.

$$

Decision Variables

S: # of Skirts to make per day

D: # of Dresses to make per day

C: # of sport Coats to make per day

$$

Objective Function

Maximize Total Daily Profit $($$ $/$ day$)=5$S $+17$D $+30$C

$$

Constraints

Cutting Time:$1$S $+3$D $+4$C $100$ hours

Sewing Time:$1$S $+4$D $+6$C $180$ hours

Material:$1$S $+1$D $+4$C $60$ yds

Non$-$negativity: S$,$ D$,$ C $0$

$$

Sensitivity Report

Variable Cells

$$

$$

Final

Reduced

Objective

Allowable

Allowable

Cell

Name

Value

Cost

Coefficient

Increase

Decrease

$B$$1$

S

$0$

$-2\mathrm{.}5$

$5$

$2\mathrm{.}5$

$1$E$+30$

$B$$2$

D

$20$

$0$

$17$

$5\mathrm{.}5$

$9\mathrm{.}5$

$B$$3$

C

$10$

$0$

$30$

$38$

$7\mathrm{.}333333333$

Constraints

$$

$$

Final

Shadow

Constraint

Allowable

Allowable

Cell

Name

Value

Price

R$.$H$.$ Side

Increase

Decrease

$B$$7$

Cutting

$100$

$4\mathrm{.}75$

$100$

$32$

$40$

$B$$8$

Sewing

$140$

$0$

$180$

$1$E$+30$

$40$

$B$$9$

Material

$60$

$2\mathrm{.}75$

$60$

$40$

$26\mathrm{.}66666667$

$$

a$)$ If the coefficient of S increases by $$2$ in the objective function, will the optimal values of S$,$ D$,$ C change?$($Yes $/$ No$)$

$$

b$)$ If the coefficient of D decreases by $$6$ in the objective function, will the optimal values of S$,$ D$,$ C change?$($Yes $/$ No$)$

$$

c$)$ If Cutting Capacity increases by $20$ hours, how much will the optimal profit increase by$?$ $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$

d$)$ If the Sewing Capacity decreases by $20$ hours, how much will the optimal profit decrease by$?$ $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$

e$)$ How much should the coefficient of S increase by in the objective function, in order to see a positive optimal value of S$?$ $$\_\_\_\_\_\_\_\_\_\_$