Question

The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 450 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 1 dollar increase in rent. Similarly, one additional unit will be occupied for each 1 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Answer 1

have you came up with your revenue function?

Answer 2

Let the rent be "x" dollars above $450.
Rent = (450 + x)
Number of apartment rented will be (100 - x)
Revenue = (450 + x)(100 - x)
What x will give maximum revenue?

If x is positive, the rent should be increased. If x is negative the rent should be decreased. Once you find x, add it to $450 to find the rent to charge.