solution

Assume that the quantities of two goods (A and B) produced by a multiproduct firm are given by the functions qA = f (pA,pB) = 10pB −10pA and qB = g(pA,pB) = 100+10pA −20pB, where qA, qB, pA, and pB denote the quantity of A produced, the quantity of B produced, the price per unit (in dollars) of A, and the price per unit (in dollars) of B, respectively. The average cost of producing A is $1 and the average cost of producing B is $2. Find pA, and pB that will maximize the firm’s total profit, . Also find the profit-maximizing levels of qA and qB and the maximum profit.

 
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