Optimization for calculus
The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 300 dollars per month. A market survey suggests that, on average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent.

Let the rent on an apartment be x dollars per month, and let N be the number of apartments rented each month, and let R be the revenue (the gross income) brought in each month by the apartment manager.

Question

Optimization for calculus
 The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 300 dollars per month. A market survey suggests that, on average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent.

Let the rent on an apartment be x dollars per month, and let N be the number of apartments rented each month, and let R be the revenue (the gross income) brought in each month by the apartment manager.