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)=200−0.5x is the unit price. Find the maximum revenue.

Answer 1

price = p= 200-x/2 where x = number of bicycles sold

Revenue = R = px = 200x-x^2/2

take the derivative and set it equal to zero, solve for x

R'= 200-x = 0

x= 200 bicycles

max R = 200(200) - (200)^2/2 =40000-20000 = $20,000