Develop and solve a linear optimization model to determine how much of each type of perfume should be produced to maximize the net profit.

Beverly Ann Cosmetics 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 be Summer Passion; the forecasted monthly demand is 7,000 bottles, and is estimated to increase by 8 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 $42.00 per bottle, and Lavender Breeze for $30.00 per bottle. A monthly budget of $100,000 is available for both advertising and purchase of the fragrances. Develop and solve a linear optimization model to determine how much of each type of perfume should be produced to maximize the net profit.


 

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