Problem: The Sonoma Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $0.90 to produce a jar of applesauce and $0.65 to produce a bottle of apple juice. The company has a policy that at least 25 percent but no more than 80 percent of its output must be applesauce.
The company wants to meet but not exceed the demand for each product. The marketing manager estimates that the demand for applesauce is 5000 jars, plus an additional 4 jars for each $1 spent on advertising for applesauce. The demand for apple juice is estimated to be 4000 bottles, plus an additional 5 bottles for every $1 spent on advertising for apple juice. The company has $19,750 to spend on producing and advertising its two products. Applesauce sells for $1.97 per jar, and apple juice sells for $1.47 per bottle.
Formulate a linear optimization model to help the company determine how many units of each product to produce, and how much advertising to spend on each product, in order to maximize profit. (You do not need to find the optimal solution).