# A market survey suggests that, on the average, one additional unit will remain vacant for each 3 dollar increase in rent. Similarly, one additional unit will be occupied for each 3 dollar decrease in rent. What rent should the manager charge to maximize?

##### 1 Answer

There is not enough information provided to give a dollar value answer.

#### Explanation:

In order to give a numerical answer, we need to know what base we are increasing/decreasing rent from and what number of units are rented at that base rent.

Let

To maximize Revenue (which I assume is what we want to maximize), apply

(If this is a positive number, increase the rent, if negative decrease it.)

Let

The number of units occupied at rent

The Revenue will be:

# = BN-Bk+3Nk-3k^2#

Maximize as usual. (Find and test the critical numbers -- or use your knowledge of quadratic functions)

The second derivative test tells us that