Average and marginal profit Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. The profit P(x) of selling x items is P(x) = xp(c) - C(x) (revenue minus costs). ​The​ average profit per item when x items are sold is P(x)/x and the marginal profit is dP/dx. The marginal profit approximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions C and price functions p.

a. Find the profit function P.

C(x) = −0.02x²+50x+100, p(x)=100−0.1x, a=500