• Oct 16th 2009, 10:12 AM
almiller08
i am at a road block with this problem and really need help plz

A company manufactures and sells x air conditoners per month. the monthly cost and price-demand equations are
C(x) = 180x + 20,000
p = 220-0.001x 0<x<100,000

how many air conditioners should the company manufacture each month to maximize its monthly profit??
• Oct 16th 2009, 01:28 PM
CaptainBlack
Quote:

Originally Posted by almiller08
i am at a road block with this problem and really need help plz

A company manufactures and sells x air conditoners per month. the monthly cost and price-demand equations are
C(x) = 180x + 20,000
p = 220-0.001x 0<x<100,000

how many air conditioners should the company manufacture each month to maximize its monthly profit??

Profit is revenue minus costs so:

$\displaystyle Pr(x)=x\times p(x)-C(x)=220x-0.001x^2-180x-20000$

Which you maximise by taking its derivative with respect to $\displaystyle x$, setting that to zero and solving for $\displaystyle x$ (the sales at which profit is a maximum).

CB