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The manager of a 90-unit apartment complex knows from experience that at a rent of...

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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 xrepresent 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) = -30x +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.)

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