A company operates two plants which manufacture the same item and whose total cost functions are $$C_1 = 6.5 + 0.01 q_1^2 \quad\mbox{and}\quad C_2 = 4.4 + 0.03 q_2^2,$$ where $q_1$ and $q_2$ are the quantities produced by each plant. The total quantity demanded, $q = q_1 + q_2$ , is related to the price, $p$ , by $$p = 80 - 0.03 q.$$ How much should each plant produce in order to maximize the company's profit?

$q_1 =$
$q_2 =$

Adapted from M. Rosser, Basic Mathematics for Economists, p. 318 (New York: Routledge, 1993).