Maximum Revenue

Question

The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 496 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar increase in rent. Similarly, one additional unit will be occupied for each 4 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Answer 1

Hello, Victoria,

I took the monthly rent times the number of units to determine total income for several scenarios. For each $4 increase or decrease in the rental rate, I decreased or increased the number of rented units by one. Graphed, this appears as an inverted curve, with a maximum income of $59,536 when 122 units are rented for $488/month. But this raises the question of how many units are available? If there are only 120, and they are all already occupied, then this is not a possible answer. The maximum profit would be to leave the rate at $469/month, since any increase in rent will result in an overall negative impact. The increased income from the other 119 units (x $4 = $476) is not enough to cover the loss of one unit of $496/month.

The number of available units isn't stated, which makes this just a guess at what the question really wants.

Bob