Question

A bus service carries 10 000 people daily between Ajax and Unoin Station, and the company has space to serve up to 15 000 people per day. The cost to ride the bus is 20$. Market research shows that if the fare increases by $0.50, 200 fewer people will ride the bus. What fare should be charged to get the maximum revenue, given that the bus company must havve at lease $130 000 in fares a day to cover operating costs?

This question I HAVE NO IDEA how to do, can you please show me step by step so it will be easier to understand for me :) THANKYOU SOOO MUCH!

Answer 1

let the number of 50 cents increases be n

NOW:
number of riders = 10000
cost per ride = 20

after increase
number of riders = 10000- 200n
cost per ride = 20+ .5n

Revenue = (10000-200)(20 + .5n)

expand this and you will have a quadratic representing a parabola that opens downwards.
So the vertex will be a maximum point representing revenue

Use whatever method you learned to find the vertex