Question

All 100 units of a storage facility will be occupied if the monthly rent is $400. For each $5 increase in monthly rent, one additional unit will remain vacant. What monthly rent should be charged per unit to maximize revenue?

Answer 1

$450

Explanation:

The number rented (q) as a function of the price (p) is ...

q = 100 -(p-400)/5 = 180 -p/5

Then the monthly revenue is ...

r(p) = pq = p(180 -p/5) = (1/5)(p)(900 -p)

This equation describes a downward-opening parabola with zeros at p=0 and p=900. The p-coordinate of the vertex of the parabola (price for maximum revenue) is halfway between these zeros, at p=450.

To maximize revenue, monthly rent should be $450.

_____

Maximum revenue will be 90·$450 = $40,500. Revenue is currently $40,000.