1. ## Maximum profit question

it costs you 10 euros per backpack to manufacture and distribute backpacks.if the backpacks sell at x euros each (where 15=or< x=or<100) the number sold is given by
n=a/x-10+b(100-x),
where a and b are positive constants.what selling price will bring a maximum profit?

2. ## Re: maths help!!!!!!!!!!!!!!!!!!!!

What have you tried here?

To find a maximum with these types of problems often require you finding a derivative and solving for the zeros.

3. ## Re: Maximum profit question

Originally Posted by university
it costs you 10 euros per backpack to manufacture and distribute backpacks.if the backpacks sell at x euros each (where 15=or< x=or<100) the number sold is given by
n=a/x-10+b(100-x),
where a and b are positive constants.what selling price will bring a maximum profit?
Profit = price*number sold - cost of production

In this case $x$ is the cost of producing one unit so the cost of produceing $n$ units is $x\times n$, so you end up with and the profit on one unit is $(x-10)$:

Profit= $(x-10)\left[\frac{a}{x-10}+b(100-x)\right] -10x$

Now when you simplify the right hand side of the above you will end up with a quadratic expression in $x$, and you have to find the maximum of this subject to the constraints on x.

(the last part can be done without calculus by completing the square)

CB

4. ## Re: maths help!!!!!!!!!!!!!!!!!!!!

Originally Posted by pickslides
What have you tried here?

To find a maximum with these types of problems often require you finding a derivative and solving for the zeros.
This is a problem in finding the maximum of a quadratic, no calculus required.

CB