Question

Demand for an electric fan is related to its selling price p (in dollars) by the equation n = 3680 − 80 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

The price of $23 will maximize the total revenue.

Step-by-step explanation:

Revenue is a function of price multiplied by quantity. Thus, the equation for revenue is,

Let p be the price.

Revenue = (3680 - 80p) * p

Revenue = 3680p - 80p²

To find the price that will maximize the revenue, we need to take the derivative of this equation as derivative tell us about change.

Taking derivative,

d/dp = 1 * 3680 - 2 * 80p

0 = 3680 - 160p

160p = 3680

p = 3680 / 160

p = 23

So, at price p=$23, the total revenue will be maximized.