please help!

[kelsey2014]

The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 400 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 5 dollar increase in rent. Similarly, one additional unit will be occupied for each 5 dollar decrease in rent. What rent should the manager charge to maximize revenue?

i know i have to create a linear equation. but it doesn't seam to match with the answer key

 

[galactus]

Let x be the number of $5 increases or decreases.

This forms a quadratic equation, not a linear one.

If the rent is raised $5, then the revenue is \(\displaystyle R(x)=(80-x)(400+5x)\)

If it is lowered $5, then the revenue is \(\displaystyle R(x)=(80+x)(400-5x)\)

If we differentiate either one we get \(\displaystyle R'(x)=-10x\)

Setting tbis to 0 and solving for x is obviously x=0.

There should be no increases or decrease in the rent because either way would result in a decrease in revenue.

 

[kelsey2014]

wow! thank you!. my answer was just 400. that makes me so mad!. but thanks for the help.