Question

The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $900 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue

Answer 1

Answer:

$950 in order to maximize the revenue.

Explanation:

The computation of monthly rent in order to maximize revenue is shown below:-

R (x) = Rent price per unit × Number of units rented

= ($900 + $10 x) × (100 - x)

= $90,000 - 900 x + 1000 x - 10 x^2

R (x) = -10 x^2 + 100 x + $90,000

Here to maximize R (x), we will find derivative and equal it to zero

R1 (x) = -20 x + 100 = 0

20 x = 100

x = 5

Therefore the monthly rent is p(5) = $900 + 10(5)

= $900 + 50

= $950 in order to maximize the revenue.