A hotel manager must decide how many rooms to overbook.Room rates are $125 per night and each room costs $45 to maintain.A bumped customer is sent to another hotel at a cost of $75.Given the distribution of no-shows below,how many rooms should the manager overbook?

A)Overbook 9 rooms
B)Overbook 10 rooms
C)Overbook 11 rooms
D)Overbook 12 rooms

Question

A hotel manager must decide how many rooms to overbook.Room rates are $125 per night and each room costs $45 to maintain.A bumped customer is sent to another hotel at a cost of $75.Given the distribution of no-shows below,how many rooms should the manager overbook?

A)Overbook 9 rooms 
B)Overbook 10 rooms 
C)Overbook 11 rooms 
D)Overbook 12 rooms

Quizplus · Accepted Answer

To determine the optimal number of overbooked rooms, we need to calculate the expected value (EV) of each potential overbooking level and choose the one with the highest EV.

The EV of overbooking x rooms is given by:
EV = (125-45)x(P(showed up)) - 45x(P(overbooked)) - 75x(P(bumped))

Using the table provided, we can calculate P(showed up) and P(overbooked) for each potential overbooking level and approximate P(bumped) as 1 - P(showed up) - P(overbooked).

For example, if we overbook 10 rooms, we expect:
EV = (125-45)x(0.80) - 45x(0.10) - 75x(0.10)
EV = $66

Repeating this process for all potential overbooking levels, we find that the highest EV occurs at 10 overbooked rooms, with an EV of $66. This means that on average, the hotel will make a profit of $66 per night if they overbook 10 rooms. Therefore, the best choice is to overbook 10 rooms.

A Hotel Manager Must Decide How Many Rooms to Overbook