COLLEGE MATH HELP

Question

A local hotel rented 450 rooms two nights ago when they charged $75 for each room. The following night they rented 600 rooms when they lowered the price to $60 per room. Assuming that this rate of change continues find the following:

 

Question 1: The owner has decided that as long as he makes at least $30,000 per night it makes sense to keep the hotel open. Find the prices the hotel should charge per room to have a revenue of at least $30,000 per night?

 

Question 2: What is the maximum revenue the hotel could expect to make in one night? 

Answer 1

the solution to this problem is to make a graph, and plot the data that is given. Place the room rate on the Y axis, and the occupancy on the X axis. the formula for a straight line on a graph is y = mx + b where y = room rate, m = slope of the line, and b = the intercept on the Y axis. in this case, the slope is $-15/150 = -10

 

we can then compose a table of room price versus occupancy based on the data in the problem

 

granted, there are only two data point pairs to plot on an X-Y graph, but it can be estimated that

 

rental fee per room           $90        $75       $72.50       $60        $45       $37.50

number of rented rooms    300        450         525          600        750        800        

gross revenue                 $27,000  33,750    41,688     36,000    33,750   30,000

 

from this table, it can be seen that the minimum nightly rental will be $37.50 per room

 

maximum revenue will occur at a room rental of $72.50 (approximately)