Question

a hotel with 440 rooms is filled to capacity when the room charge is $60 per night. for each $2 increase in room charge, 5 fewer rooms are filled each night. what charge per room will result in the maximum revenue per night?

Answer 1

To find the charge per room that will result in the maximum revenue per night, we need to determine the optimal number of rooms to fill.

This occurs when the number of rooms filled is at a maximum. So, the charge per room that will result in the maximum revenue per night is $70.

Step-by-step explanation:

We can start by creating a table to represent the relationship between the room charge and the number of rooms filled:

Room charge Number of rooms filled

$60 440

$62 435

$64 430

$66 425

...... ..... .....

As the room charge increases by $2, the number of rooms filled decreases by 5. From the table, we can see that the revenue per night is the product of the room charge and the number of rooms filled.

To find the charge per room that will result in the maximum revenue per night, we need to find the point where the revenue is maximized. This occurs when the number of rooms filled is at a maximum.

Looking at the table, we can observe that as the room charge increases, the number of rooms filled decreases until it reaches 5.

So, the charge per room that will result in the maximum revenue per night is $60 + ($2 x 5) = $70.