Calculus Problem

Question

The demand for thousands of "Zombie Death Bats" (patent pending) is given by D(p) = 124*exp(-0.0023*p), where p is the price in dollars.

At what price should the "Zombie Death Bats" be sold to maximize the Revenue?

Answer 1

Revenue R(p) = p D(p) = 124 p e^-0.0023p

dR/dp = 124 e^-0.0023p - 0.2852 p e^-0.0023p = e^-0.0023p ( 124 - 0.2852p)

We need dR/dp = 0

The term involving e is always strictly positive, so can't be zero

so we need 124 - 0.2852p = 0, giving p = $ 434.78