Calculus
posted by John .
The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 472 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?

d unit/drent= 1unit/4dollars rent.
revenue=80+x)(4724x)
drevenue/dx=4(80+x) + (4724x)=0
240+4x472=4x
8x=232
x=29 units, so rent should be 4724*29
check that.