# Word problem

• Jun 9th 2009, 07:47 PM
hemi
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.
• Jun 9th 2009, 08:11 PM
Random Variable
solve $\displaystyle \frac {dP}{dx} = 0$ to find the critical points
• Jun 13th 2009, 07:11 PM
hemi
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 ?
• Jun 15th 2009, 05:43 AM
stapel
If the profit value is increasing up to a certain x-value, and then decreasing after that x-value, where then would be the maximum value of P? (Wink)