# Thread: MAXIMUM PROFIT (multiple variables)

1. ## MAXIMUM PROFIT (multiple variables)

Sadly i do have one more i thought the last question would make more sense of this one unfortunately it did not...

So if you could be so kind here it is...

It costs you c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars each, the number sold given by
$\displaystyle n=(a/(x-c))+(b(100-x))$
where a and b are certain positive constants.
what selling price will bring a maximum profit?

in my notes to find the max profit one would have to have two seperate functions find their derivatives and have them = to each other... like in my last question.
The issue here is that there is only one function.
also what is supposed to be the marginal revenue

i am sorry if this is obvious and i am just not missing it.. but something does not seem to add up to me.

thank you so very much...again

2. Originally Posted by Audriella
Sadly i do have one more i thought the last question would make more sense of this one unfortunately it did not...

So if you could be so kind here it is...

It costs you c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars each, the number sold given by
$\displaystyle n=(a/(x-c))+(b(100-x))$
where a and b are certain positive constants.
what selling price will bring a maximum profit?

in my notes to find the max profit one would have to have two seperate functions find their derivatives and have them = to each other... like in my last question.
The issue here is that there is only one function.
also what is supposed to be the marginal revenue

i am sorry if this is obvious and i am just not missing it.. but something does not seem to add up to me.

thank you so very much...again
P = nc - nx = n(c - x).

Substitute for n and solve dP/dx = 0. Test the nature of all solutions - you want the minimum.