Using Sensitivity Information Correctly

$36.$ B$$verly Anin Cosmetics has created two new perfumes: Summer Passion and Ocean Breeze. It costs $$5\mathrm{.}25$ to purchase the fragrance needed for each bottle of Summer Passion and $$4\mathrm{.}70$ for each bottle of Ocean Breeze. The marketing department has stated that at least $30\%$ but no more than $70\%$ of the product mix be Summer Passion; the forecasted monthly demand is $7,000$ bottles and is estimated to increase by eight bottles for each $$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 information is misleading because it violates the assumptions of sensitivity analysis.