Question

A sports store sells 42 pairs of running shoes per day for $ 10.00 each. The owner estimates that for each $ 2.00 increase in price, 2 fewer sales are made each day. What price should be charged to maximize profit?

Answer 1

Answer: $26

Explanation:

Let the number of $2 price increases be x.

This means that if the price is 10+2x, 42-2x shoes are sold.

So, the revenue is (10+2x)(42-2x).

To maximize profit, we must maximize revenue.

`(10+2x)(42-2x)\\\\=-4x^2 +64x+420`

The maximum is at
`x=-(64)/(2(-4))=8`, so the price should be 10+2(8)=$26.