The question:

You are the manager of a 100-unit apartment building. The average monthly maintenance cost per occupied unit is $100. You ordered a survey that revealed that all units can be rented when the rent, r is $900, and that one unit will become vacant with each $10 increase in rent.

a) Find a fuction that gives you the number of units rented n, as a function of r.

b) The revenue is the total amount of money you receive by renting the apartments. Find the revenue fuction.

c) The net cash intake is the revenue minus the maintenance. Find a formula for the net cash intake.

d) Determine the rent that will maximize the net cash intake.

The problem is I don't know where to start. There are no examples of this particular problem in my book (that I nor my classmates can find) and the first part seems too simple. Could the function for a be as simple as:

a) f(r) = rn; or perhaps f(r) = r100; or f(r) = r100 - 1000

b) R(n) = 900n -1000

c)C(n) = (910)(n-1) - 1000-1

R=Revenue, C=Cash

I don't know the best way to approach this problem.