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

profit = revenue  cost
revenue = demand * price
profit is thus x(3004x)  (500+28x)
= 4x^2 + 272x  500
This a parabola with vertex at (34,4124)
So, max profit is 4124 when x = 34