Chapter 4.3, Problem 19E

Production Costs A brewery produces regular beer and a lower-carbohydrate “light” beer. Steady customers of the brewery buy 10 units of regular beer and 15 units of light beer monthly. While selling up the brewery to produce the beers, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular beer is $32,000 and the cost per unit of light beer is $50,000. Every unit of regular beer brings in $120,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery wants at least $9,000,000 in revenue. At least 20 additional units of beer can be sold.

(a) How much of each type of beer should be made so as to minimize total production costs?

(b) Suppose the minimum revenue is increased to $9,500,000. Use shadow costs to calculate the total production costs.