A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to the price P, in dollars, of an oven by the fu

Question

A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to the price P, in dollars, of an oven by the function R(P) = 85P – 0.25P2. What price will give the maximum revenue?

Answer 1

Since the revenue R(P) = 85*P - 0.25*P^2 is a quadratic function its maximum is attained for the price P that makes the first derivative vanish, i.e., when

 

R'(P) = 85 - 0.5*P = 0

 

Hence, P = 170.