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)=400−0.25x is the unit price. Find the maximum revenue.

Answer 1

The revenue is:

R(x) = 400x-0.25x²

This is the equation for a parabola. The maximum can be found at the vertex of the parabola using the formula:

x=-b/2a from the parabolic equation ax²+bx+c where a=-0.25, b=400 for this case

x = -400/(2(-0.25)) = 400/0.5 = 800

R(800) = 400(800)-800²/4 = 240000 - 640000/4 = $80000