The manager of an 80-unit apartment complex is trying to decide what rent to charge. Experience has shown that at a rent of $800, all the units will be full. On the average, one additional unit will remain vacant for each $25 increase in rent.

a. Let x represent the number of $25 increases. Find an expression for the rent for each apartment.

b. Find an expression for the number of apartments rented.

c. Find an expression for the total revenue from all rented apartments.

d. What value of x leads to maximum revenue?

e. What is the maximum revenue?