The revenue function for a sporting goods company is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=400−0.4x is the unit price. Find the maximum revenue.

Answer 1

P(x) = 400 -0.4x

R(x) = xP(x) = 400x -0.4x^2

take the derivative and set it equal to zero

R'(x) = 400 -0.8x = 0

x = 400/0.8 = 2000/4 = 500 units

R(500) = 400(500) - 0.4(500)^2

= 200,000 - 0.4(250,000)

=$100,000 = maximum Revenue

The revenue function is graphically a downward opening parabola with vertex = maximum point at (500, 100,000)

R(501) = 400(501)-0.4(501)^2 = 200400-100400.4=99,999.6

sell slightly more or slightly less than 500 units and revenue goes below $100,000