SOLUTION: hi, I was going through my math homework and i was wondering if you could help me with this problem… A model for a company's revenue is R=-15p^2+300p+12,000 where P is the pri

Algebra ->  Finance -> SOLUTION: hi, I was going through my math homework and i was wondering if you could help me with this problem… A model for a company's revenue is R=-15p^2+300p+12,000 where P is the pri      Log On


   

Question 833705: hi,
I was going through my math homework and i was wondering if you could help me with this problem…
A model for a company's revenue is R=-15p^2+300p+12,000 where P is the price in dollars of the company's product. What price will the maximum revenue? find the maximum revenue.
Thanks so much for your time and help!

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find the p value for the vertex and then and use it to compute R. You may also want to try completing the square to put R into standard form.

highlight%28highlight%28P%3C%3Ep%29%29

A process for finding p of the vertex:
-15p%5E2%2B300p%2B12000=0, because this is a way to find the p intercepts, assuming p is on a horizontal number line...
Divide both sides by 15...
-p%5E2%2B20p%2B800=0
%28-1%29%28p%5E2-20p-800%29=0
%28-1%29%28p-40%29%28p%2B20%29=0
The p intercepts are -20 and 40. The middle value of this is highlight_green%28%28-20%2B40%29%2F2=highlight%2810%29%29. This means that the vertex occurs at highlight%28p=10%29.
-
The maximum revenue, highlight%28R=-15%2A10%5E2%2B300%2A10%2B12000%29