Question

The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 474 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 1 dollar increase in rent. Similarly, one additional unit will be occupied for each 1 dollar decrease in rent. What rent should the manager charge to maximize revenue? Hint: Let x be the number of 1 dollar increases (or decreases) in rent. Write the rental price as a function of x and write the number of units rented as a function of x. Use these to write the revenue.