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.