Question

Demand for an electric fan is related to its selling price p (in dollars) by the equation n = 1960 − 70 p where n is the number of fans that can be sold per month at a price p . Find the selling price that will maximize the revenue.

Answer 1

$14

Explanation:

The revenue from sales of fans is the product of the number of fans sold and the price at which they are sold:

R(p) = n·p = (1960-70p)p

R(p) = 70(28 -p)p

This equation describes a parabola that opens downward and has zeros at p=0 and p=28. The axis of symmetry is halfway between those zeros, at p=14. It goes through the vertex or point of maximum revenue.

The price for maximum revenue is p = 14 dollars.