Take Home Exam Problem $$ Sensitivity Analysis

Given the following Product Mix Linear Programming Problem and Excel Solver Solution:

Maximize Profit $=15$X$1+20$X$2+14$X$3$

Subject to:

$5$X$1+6$X$2+4$X$3<210($hours of Resource $1)$

$10$X$1+82$X$2+5$X$3<200($hours of Resource $2)$

$4$X$1+2$X$2+5$X$3<170($hours of Resource $3)$

Xi $>0$

Microsoft Excel $14\mathrm{.}0$ Sensitivity Report

Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$$3$ Product $10-10\mathrm{.}61510\mathrm{.}6---$

$C$$3$ Product $250202\mathrm{.}410\mathrm{.}6$

$D$$3$ Product $332014361\mathrm{.}5$

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R$.$H$.$ Side Increase Decrease

$E$$6$ Resource $11580210---52$

$E$$7$ Resource $22002\mathrm{.}420070\mathrm{.}130$

$E$$8$ Resource $31700\mathrm{.}417030120$

How does Profit change under each of the following changes:

a$.$ The price of Product $2$ goes up by $$2?+$$$2(5)$

b$.$ The price of Product $3$ goes down by $$1?-$$$1(32)$

c$.$ The price of Product $1$ goes up by $$8?0$

d$.$ The available hours of Resource $1$ increase by $40$ hours?

e$.$ The available hours of Resource $2$ decrease by $20$ hours?

f$.$ The available hours of Resource $1$ decreases by $60$ hours?