A train service carries 20,000 people daily between Rationalia and Real City. The rail line could serve up to 60,000 people. The cost to ride the train is $, but research shows that for each fare increase of $0.02, ridership will go down by 271 people.

a) Create a function to represent the revenue of the train service after x increases of $0.02.

b)Given the constraints of the problem, what is the domain of your function?

c)What fare should be charged to maximize revenue?

d)If each rider costs the rail service $0.10, what fare should be charged to maximize profit?