Hello!

I have to answer a question that reads as follows:

A real-estate firm owns 100 garden-type apartments. At $400 per month, each apartment can be rented. However, for each $10 per month increase, there will be two vacancies with no possibility of filling them. Let the monthly rent per apartment be x, with x >= 400

(a) How many apartments are rented if the rent x = 450 ?

(b) Find a general expression of the number of apartments rented n=n(x) if the rent is x. What is monthly revenue R=R(x)?

(c) What rent per apartment will maximize monthly revenue R?

I am quite stuck. I've tried writing out all the bits of data, but have no luck.

I made a chart like this:

Cost of 400 = 100 units rented = Revenue of 40000

Cost of 410 = 98 units rented = Revenue of 40180

Cost of 420 = 96 units rented = Revenue of 40320

Cost of 430 = 94 units rented = Revenue of 41280

Cost of 440 = 92 units rented = Revenue of 40,480

Cost of 450 = 90 units rented = Revenue of 40,500

I can see the revenue function will probably be quadratic. And I know the answer to (a), as you can see by the chart. But the rest has me quite frantic.

Any help would be greatly appreciated.

Thanks,

- Jon Nash