Find the maximum revenue

Question

The revenue function for a lawnmower shop is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=700−0.5x is the unit price. Find the maximum revenue.

Answer 1

R = 700x -0.5x^2 = price times quantity sold

take the derivative and set it equal to zero for the revenue maximizing amount sold

R' = 700 -x =0

x =700 for maximum revenue

R(700) = 700(700) - 700^2/2 = 490,000/2 = $245,000