The Andrews Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $0.80 to produce a jar of applesauce and $0.60 to produce a bottle of apple juice. The company has a policy that at least 20 percent but not more than 60 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 a maximum of 5,000 jars, plus an additional 3 jars for each $1 spent on advertising for applesauce. The maximum demand for apple juice is estimated to be 4,000 bottles, plus an additional 5 bottles for every $1 spent on advertising for apple juice. The company has $16,000 to spend on producing and advertising its two products. Applesauce sells for $1.75 per jar; apple juice sells for $1.75 per bottle. The company wants to know how many units of each product to produce, and how much advertising to spend on each product, in order to maximize profit.
a. What are the optimal quantities of apple sauce and apple juice for Andrews to produce? (Rounding off is acceptable.)
b. What is the optimal amount to spend on advertising? What is the optimal profit?
c. Describe the qualitative pattern in the solution.