
Word problem
Hi,
I need some assistance with the following word problem :
The profit $\displaystyle P$ made by a cinema from selling $\displaystyle x$ bags of popcorn can be modeled by:
$\displaystyle P = 2.36x  \frac{x^2}{25000}  3500, 0 < x < 50000$
NOTE: the $\displaystyle <$ is suppose to be also "or equal to" i just didn't know the syntax.
I need to:
a  Find the intervals on which [tex]P[/math is increasing and decreasing.
b  If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain please.

solve $\displaystyle \frac {dP}{dx} = 0 $ to find the critical points

Right so I did this:
$\displaystyle P'=2.36\frac{1}{12500}x = 0$
$\displaystyle x = 29500$
and I tested in the intervals : ( infinity, 29500) , (29500, infinity) and found its increasing on the first and decreasing on the second (respectively).
now how can I answer part b of my question ?

If the profit value is increasing up to a certain xvalue, and then decreasing after that xvalue, where then would be the maximum value of P? (Wink)