The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 400 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 5 dollar increase in rent. Similarly, one additional unit will be occupied for each 5 dollar decrease in rent.

Let x denote the number of 5 dollar increases in rent. Thus x=2 means monthly rent increases by 10 dollars to 410 dollars, and x=-2 means rent changes by -10 dollars to 390 dollars.

(a) Express the rent as a function of x.
f(x)=

(b) Express the number of occupied units as a function of x.
g(x)=

(c) Express the rental revenue as a function of x.
R(x)=

(d) What rent should the manager charge to maximize revenue?