Question

The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 420 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Answer 1

Solution:

Revenue is found by multiplying number of units ? by the rent of each unit r.

If there are ? increases of 6 dollars each in the rent, then

and

And so,

with respect to ?, the maximum revenue occurs when dR/dn=0

This means that for 15 increases each of 6 dollars in the rent, revenue is maximum.

The rent is then

If there are ? decreases of 6 dollars each in the rent, then

and

And so,

with respect to ?, the maximum revenue occurs when dR/dn=0

The rent is then

Thus, the manager should charge $510 of the rent to maximize revenue.