How do I solve this?

Question

R(q)=510q and the cost function C(q)=9800+3q2. Round your answers to the nearest whole number. a) At what quantity is profit maximized? q = ? b) What is the total profit at this production level? profit = $

Answer 1

Profit function would be defined as Revenue - Cost, so p(q) = R(q) - C(q). To find when profit is maximized find the critical point of this function, this will be where the profit is maximized since its a parabola that opens downwards. Then plug in this critical point into your profit function to find the total profit at that production level.

Edit:

You should get a profit function of p(x) = 510q - 9800 -3q², the derivative of this function is p^'(x) = 510-6q, so the critical point is when the derivative is 0. We get 0 = 510-6q means q = 510/6 is a critical point.