Using Sensitivity Information Correctly

Beverly Ann Cosmetics has created two new per$-$

fumes: Summer Passion and Ocean Breeze. It costs

$$5\mathrm{.}25$ to purchase the fragrance needed for each bot$-$

tle of Summer Passion and $$4\mathrm{.}70$ for each bottle of

Ocean Breeze. The marketing department has stated

that at least $30\%$ but no more than $70\%$ of the prod$-$

uct mix be Summer Passion; the forecasted monthly

demand is $7,000$ bottles and is estimated to increase

by eight bottles for each $$1$ spent on advertising. For

Ocean Breeze, the demand is forecast to be $12,000$

bottles and is expected to increase by $15$ bottles for

each $$1$ spent on advertising. Summer Passion sells

for $$42\mathrm{.}00$ per bottle and Ocean Breeze for $$30\mathrm{.}00$

per bottle. A monthly budget of $$100,000$ is available

for both advertising and purchase of the fragrances.

a$.$ Develop and solve a linear optimization model

to determine how much of each type of perfume

should be produced to maximize the net profit.

b$.$ In viewing the Solver Sensitivity Report, explain

what information is accurate and what informa$-$

tion is misleading because it violates the assump$-$

tions of sensitivity analysis.