The manager of a 100 unit apartment complex knows from experience that all units will be occupied if the rent is $500 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue?

Answer 1

Income= rent(100-1/10*(rent-500)

d I/drent= (100-rent/10+50)-rent(1/10)=0

150=2/10 rent
rent= 750
check that

Answer 2

checking : assume 750 rent, 760 rent, and 740 rent

rent units income
750 75 56,250
740 76 56,240
760 74 56240
calculus is awesome