A company makes and ships their backpacks at $5 each.If the backpacks sell for $p each,the number sold ,x, is given by x=a/(p-10)+b(130-p),where a and b are constants.what selling price will yield the largest profit for the company

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- Dec 17th 2005, 04:11 AMbobby77need help please!
A company makes and ships their backpacks at $5 each.If the backpacks sell for $p each,the number sold ,x, is given by x=a/(p-10)+b(130-p),where a and b are constants.what selling price will yield the largest profit for the company

- Dec 17th 2005, 05:45 AMCaptainBlackQuote:

Originally Posted by**bobby77**

RonL - Dec 17th 2005, 09:52 AMCaptainBlackQuote:

Originally Posted by**bobby77**

$\displaystyle x= \frac{a}{p+10}+b(130-p)$

The profit per sale is:

$\displaystyle p-5$

so the total profit is:

$\displaystyle P=(p-5).x=(p-5). \left\{\frac{a}{p+10}+b(130-p)\right\}$

Now the usual way to find the maximum total profit is to differentiate $\displaystyle P$ wrt

the price $\displaystyle p$ and then set the result to zero. Then solve for the price which

maximises the profit. Which is what you have to do here.

You should normaly check that the solution/s is/are maxima or minima just

to be sure.

RonL