SOLUTION: David owns a block of 30-holiday units that he rents out. He estimates that 90% of the units are occupied when he charges $250 rent per unit per night. David finds that if he incre

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Question 1152845: David owns a block of 30-holiday units that he rents out. He estimates that 90% of the units are occupied when he charges $250 rent per unit per night. David finds that if he increases the rent, the demand for the units decreases. For each $40 increase in the charge, three more units are not occupied.
a) Express the number of units occupied as a function of the rent charged.
b) Express the total revenue obtained by David as a function of the rent charged.

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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(a)  Let p be the price for one single unit, and let  d(p)  be the number of occupied units as the function of price.


    The condition says that


        d(250) = 0.9*30 = 27  units,   and

        d(p) = 27 - 3%2A%28%28p-250%29%2F40%29.        (1)


    Formula (1) is the answer to question (a).



(b) Total revenue is the product of the number occupied units by the price per unit


       R(p) = d(p)*p = [ 27 - 3%2A%28%28p-250%29%2F40%29%29 ]*p.    (2)


    Formula (2) is the answer to question (b).


    You can simplify and transform this formula by any of equivalent ways.