SOLUTION: 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. Mar

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.

RELATED QUESTIONS
Could someone please show me how to find the equation of a line that passes through... (answered by stanbon)

A person invests 600.00 at 5.64% compounded continously. How long will it take for the... (answered by scott8148,bucky)

So I am really stumped on this problem. I am having a hard time drawing it on here for... (answered by Edwin McCravy)

Use the model for the period of a pendulum, T, such that T = 2π sqrt (L/ g),... (answered by ikleyn)

Find the common logarithm by using the calculator. 1.174^-4. I am nor quite sure how to... (answered by Alan3354)

Divide the first polynomial by the second. 6x^3-19x^2+x=6 and x-3 I am not sure how to (answered by vleith)

I have to solve this equation by completing the square, and I'm a bit stumped. Any help... (answered by jim_thompson5910)

Hello, I am having a really hard time with these problems. What is the proper way to set (answered by ptaylor)

I do not know how to solve a negative absolute value equation and am looking for help on... (answered by jim_thompson5910)