1. ## Optimization of Revenue

The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 490 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent. What rent should the manager charge to maximize revenue?
Ok for this I have set up the following:

My webwork says I'm wrong so can someone help me identify what I did wrong?
Thanks

R(x) = (80-x)(490+7x)
dR/dx = -(490 + 7x) + 7(80-x)
0 = -490 - 7x - 7x + 560
14x= 70
x= 70/14

Now I did (490 + 7(70/14))

2. ## Re: Optimization of Revenue

Originally Posted by habibixox
The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 490 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent. What rent should the manager charge to maximize revenue?
Ok for this I have set up the following:

My webwork says I'm wrong so can someone help me identify what I did wrong?
Thanks

R(x) = (80-x)(490+7x)
dR/dx = -(490 + 7x) + 7(80-x)
0 = -490 - 7x - 7x + 560
14x= 70
x= 70/14

Now I did (490 + 7(70/14)) = 490 + 35 = 525
and got 520
...