Question 762313: I'm drawing a blank at how to set this equation up - any help would be greatly appreciated!
A city's transit authority serves 156,000 commuters daily when the fare is $1.50. Market research has determined that every penny decrease in the fare will result in 1,200 new riders. What fare will maximize revenue?
Thank you!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A city's transit authority serves 156,000 commuters daily when the fare is $1.50. Market research has determined that every penny decrease in the fare will result in 1,200 new riders. What fare will maximize revenue?
-------------------------
R(x) = (150-x)(156000+1200x)
----
R'(x) = (150-x)*1200 + 156000*(-1)
---
Solve: 1200(150-x) - 156000 = 0
-----
1200x = 1200*150 -156000
-----
x = 20 cents
===================
Max fare = $1.50 - 20 = $1.30
======================
Cheers,
Stan H.
|
|
|
