The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 324 dollars per month. A market survey suggests that, on the av- erage, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. What rent should the manager charge to maximize revenue?
The revenue is :R= number of units*rent per month. Let x is the number of additional units, then R(x)=(80-x)(324+6x)=25920+156x-6x^2. The revenue maximize when the derivation of R(x)=0. (dR/dx)=156-12x=0 x=13 The rent is 324+13*6=402 dollars