1. ## Revenue Word Problem

I really have no idea where to even begin with this word problem:

You buy an apartment building with 40 units. The previous owner charged $420 per month for a single apartment and, on average, rented 30 apartments at that price. You discover that for every$30 you raise the price of rent, another apartment stands vacant because someone can't afford it. What price should you charge for an apartment in order to maximize your revenue?

Any help would be appreciated

2. Originally Posted by maryanna91
I really have no idea where to even begin with this word problem:

You buy an apartment building with 40 units. The previous owner charged $420 per month for a single apartment and, on average, rented 30 apartments at that price. You discover that for every$30 you raise the price of rent, another apartment stands vacant because someone can't afford it. What price should you charge for an apartment in order to maximize your revenue?

Any help would be appreciated
If you let $\displaystyle N$ apartments at charge $\displaystyle C$ the revenue is:

$\displaystyle R=C \times N$

If you charge $\displaystyle C$ the number of apartments let is:

$\displaystyle N=30-(C-420)/30$

So the Revenue is:

$\displaystyle R=C[30-(C-420)/30]$

which you are to find the maximum of as $\displaystyle C$ changes, you will have to do some checking at the end to make sure you have let an integer number of apartments.

CB