business cal

almiller08 · #1 $Old$ October 16th, 2009, 12:12 PM

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??

CaptainBlack · #2 $Old$ October 16th, 2009, 03:28 PM

Quote:

Originally Posted by almiller08 $View Post$

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:

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

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

CB