College Algebra- maximum revenue

Question

The revenue function for a bicycle shop is given by R(x)=x•p(x) dollars where x is the number of units sold and p(x)=400-.2x is the Unit price. Find the maximum revenue.

Answer 1

R(x) = x(400-x/5) = 400x -(1/5)x^2

take the derivative and set equal to zero & solve for x

R'(x) = 400 -(2/5)x = 0 at the maximum level.

(2/5)x = 400

x = (5/2)400 = 1000 units sold

price = 400-(1/5)1000 = 400-200 = 200

maximum revenue is px = 200(1000) = $200,000