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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?

Respuesta :

Medunno13

Answer: $26

Step-by-step 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.

[tex](10+2x)(42-2x)\\\\=-4x^2 +64x+420[/tex]

The maximum is at [tex]x=-\frac{64}{2(-4)}=8[/tex], so the price should be 10+2(8)=$26.

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