Answer Happy

(8 points) The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 464 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decrease in rent. We will define the variable a to represent the number of rate increases that are included. We will allow a to be any real number, including decimal values. (a) Find the function p(a) which gives the monthly rent for an apartment (price) in dollars, where a is the number of increases. p(a) = (b) Find the function q(a) which gives the quantity of occupied apartments (the monthly demand), where a is the number of increases. q(a) = (c) Find the total revenue function R(a) which gives the total monthly revenue from apartment rentals in dollars, where a is the number of rate increases. R(a) = (d) Find the value of a that will maximize the daily revenue function R(a). Do not round your answer. The value of a to maximize daily revenue is a = (e) Use your answers above to complete the following sentences. Answers with dollar amounts should be accurate to the exact cent. In order to maximize the monthly revenue from rentals, the apartment complex manager should ? revenue, the new fee to rent an apartment for a month will be $ and generate a total revenue of $ each month. ✓the current rent for an apartment. To maximize of the apartments will be occupied. This will