A cosmetics company has created two new perfumes: Summer Passion and Ocean Breeze. It costs $5.25 to purchase the fragrance needed for each bottle of Summer Passion and $4.70 for each bottle of Ocean Breeze. The marketing department has stated that at least 30% but no more than 70% of the product mix must be Summer Passion; the forecasted monthly demand is 7,000 bottles and is estimated to increase by

nine

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

17

bottles for each $1 spent on advertising. Summer Passion sells for $42.00 per bottle and Ocean Breeze for $30.00 per bottle. A monthly budget of $100,000 is available for both advertising and purchase of the fragrances. Complete parts a and b.

Develop and solve a linear optimization model to determine how much of each type of perfume should be produced to maximize the net profit. Note that the amounts can be fractions of bottles.

The cosmetics company should produce ______ bottles of Summer Passion and ______

bottles of Ocean Breeze, and should spend ______ on advertising for Summer Passion and

______ on advertising for Ocean Breeze. The net profit is ______.

Please show work