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Maximization of Profit for Cheese Spread Manufacturing

Megley Cheese Company is a small manufacturer of several different cheese products. One of the products is a cheese spread that is sold to retail outlets.
Jason Megley must decide how many cases of cheese spread to manufacture each month. The probability that the demand will be six cases is 0.1, for 7 cases is 0.3, for 8 cases is 0.5, and for 9 cases is 0.1. The cost of every case is $45, and the price that Jason gets for each case is $95. Unfortunately, any cases not sold by the end of the month are of no value, due to spoilage. How many cases of cheese should Jason manufacture each month?

Solution Preview

Jason wishes to manufacture the number of cases of cheese spread which maximizes his expected monthly profits. There is no reason for Jason to manufacture fewer than 6 cases since he is guaranteed to sell at least that many and no reason for him to manufacture more than 9 cases since this is the most he will be able to sell. Thus, we must compute the expected profits if he manufactures 6, 7, 8, or 9 cases.

If Jason manufactures 6 cases, he is guaranteed to sell them all, so his profit will be

6 * ($95 - ...

Solution Summary

We show how a cheese salesman can maximize his profits.