# Alegebra shirt sales problem

• Dec 17th 2005, 05:11 AM
bobby77
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, 06:45 AM
CaptainBlack
Quote:

Originally Posted by bobby77
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

This looks peculiar, as your sales are $\infty$ when the selling price is $10. RonL • Dec 17th 2005, 10:52 AM CaptainBlack Quote: Originally Posted by bobby77 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

Lets assume that the sales should be:

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

The profit per sale is:

$p-5$

so the total profit is:

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

Now the usual way to find the maximum total profit is to differentiate $P$ wrt
the price $p$ 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