The manager of an 68-unit apartment building is trying to decide what rent to ch

Question

The manager of an 68-unit apartment building is trying to decide what rent to charge. Experience has shown that at a rent of $780, all the units wil be full. On average, one additional unit will become vacant for each $32 increase in rent a Let x represent the number of $32 increases. Find an expression for the total revenue R(x) eamed from all rented apartments. b. The value of x that will produce the maximum revenue is Rlound to the nearest whole number as needed.) eThe maumum revenue is SL Round to the nearest whole number as needed.) Enber your answor in each of the answer boxes %20162 728088% 203,%2o-s2oralsek 28 MacBook Pro 6 8

Explanation / Answer

$ 780 will get 65 units charge

each additional unit will increase rent by $ 32

so, revenue function can be written as

R(x) = ( 65 - x ) ( 780 + 32x )

R(x) = - 32x^2 + 1300x + 50,700

b) value of x that will maximize revenue is x = -1300/2(-32)

x = 20

c) maximum revenue is - 32(20)^2 + 1300(20) + 50,700

$ 63903

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