Calculus Homework

Question

Given revenue and cost functions

R(q)=80q−0.5q^2 C(q)=14q+600​,

find the maximum revenue that can be earned by selling this product.

The maximum revenue is

..????

Answer 1

Do you mean the maximum revenue or the maximum profit?

To find the maximum profit you first have to find the profit function P(q) = R(q) - C(q) . You then find the derivative of the Profit function P'(q) and solve for q to get the quantity that gives the maximum profit.

If you just want to find the maximum revenue you take the derivative of the revenue function and then set this equal to zero and solve for q. Let's do this!

R(q) = 80q - 0.5q²

R'(q) = 80 - q

So 80 - q = 0 so q = 80

We know plug this value of q back into the revenue function to get the maximum revenue

R(80) = 80 × 80 - 0.5 × 80² = 3200

The maximum revenue is therefore 3200