Ok, here is the problem I'm stuck on... The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 360 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue?
ehhh 585? x = rent y = # of units y = (-1/9)x + some constant so plug in the original constraints 90 = (-1/9)(360) + some constant constant = 130 so y = (-1/9)x + 130 total profit = rent * # of units P = x*y P = x*[(-1/9)x + 130] P = (-1/9)x^2 + 130x take the derivative to maximize P' = (-2/9)x + 130 set the derivative to zero to solve for x 0 = (-2/9)x + 130 x = 585 the manager should set the rent to $585/month