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 function that gives you the number of units rented n, as a function of r.
n = 100 - (r-900)/10 , r > 900
b) The revenue is the total amount of money you receive by renting the apartments. Find the revenue function.
R = rn = r[100 - (r-900)/10]
c) The net cash intake is the revenue minus the maintenance. Find a formula for the net cash intake.
C = rn - 100n = (r - 100)n = (r - 100)[100 - (r-900)/10]
d) Determine the rent that will maximize the net cash intake.
the function C is quadratic with a negative leading coefficient ... max will be at the vertex.