A dairy produces whole milk and skim milk in quantities a and
y gallons, respectively. Suppose that the price of whole milk is p(x) = 20-5x and that the price of skim milk is q (y) = 4 - 2y and assume that C (x, y) = 2xy + 4 is the total (!) joint-cost function of the commodities. What should x and y be to maximize profit, assuming that the first prder conditions yield a maximum?
