This is section 3.8 problem 30: a motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. for every $3 rise in the charge per room per day, one more room is vacant. each occupied room costs an additional $16 per day to maintain. (a) the demand function, expressed by p , the price in dollars charged for each room per day, as a function of x ,

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Explanation:

First, for 80 room charged at $60 per room ,all rooms are occupied

Let the demand function, expressed by p , the price in dollars charged for each room per day, as a function of x as,

p(x)=$60x where x in the number of rooms

When the price per room is increased by $3, the demand function will be;

p(x)=$63x

Maintenance per room after price increase will be;

p(x)=$16x

This means: $63x -$60x=$16x

3*80 p(x)=16*80

p(x)=(16*80)/(3*80) =5.33

Due to price increase the number of rooms occupied reduced by 5 rooms to 75 rooms. Because of unoccupied rooms bringing no revenue the maintenance cost increased. The demand for room decreased.

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