The price P per unit at which a company can sell all that it produces is given by the

Question

function P(x) = 300 — 4x. The cost function is c(x) = 500 + 28x where x is the number
of units produced. Find x so that the profit is maximum.

Answer 1

profit = revenue - cost
revenue = demand * price

profit is thus x(300-4x) - (500+28x)
= -4x^2 + 272x - 500

This a parabola with vertex at (34,4124)

So, max profit is 4124 when x = 34