The manager of a 90-unit apartment complex knows from

Last updated: 7/14/2022

The manager of a 90-unit apartment complex knows from experience that at a rent of $1500 per month, all units will be rented. However, for each increase of $30 ir[ rent, he can expect one unit to be vacated. Let x represent the number of $30 increases over $1500. Complete parts (a) through (e) below. (a) Express, in terms of x, the number of apartments that will be rented if x increases of $30 are made. (For example, with three such increases, the number of apartments rented will be 90-3=87.) The number of apartments that will be rented if x increases of $30 are made is 90-x. (b) Express the rent per apartment if x increases of $30 are made. (For example, if he increases rent by $90=3-$30, the rent per apartment is given by 1500+3 (30) = $1590.) The rent per apartment if x increases of $30 are made is 1500 + 30x. (c) Determine a revenue function R in terms of x that will give the revenue generated as a function of the number of $30 increases. A revenue function R in terms of x that will give the revenue generated as a function of the number of $30 increases is R(x) = -30x² +1200x + 135,000. (Simplify your answer.) (d) For what number of increases will the revenue be $142,680? The number of increases is (Use a comma to separate answers as needed.)