The Harriet Hotel in downtown Boston has 100 rooms that rent for $150 per night. It costs the hotel $30 per room in variable costs (cleaning, bathroom items, etc.) each night a room is occupied. For each reservation accepted, there is a 5% chance that the guest will not arrive. If the hotel overbooks, it costs $200 to compensate guests whose reservations cannot be honored. How many reservations should the hotel accept if it wants to maximize the average daily profit

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stokholm stokholm · Answer 1 · 2019-09-03T10:21:34+02:00

Answer:

In order to maximize average daily profit, optimal number of reservations = 100 rooms.

Explanation:

As for the provided information, we have

Total number of rooms = 100

Chances of guests not arriving = 5%

Therefore, guests to arrive = 95%

Thus, bookings = 100/95% = 105.26

Rounding off we have 105 rooms,

Let us assume, all rooms are booked and no cancellation is done, in that case,

Total revenue = $150 [tex]\times[/tex] 100 = $15,000

Less: Overbooked charges = $200 [tex]\times[/tex] 5 = ($1,000)

Less: Variable Cost = $30 [tex]\times[/tex] 100 = ($3,000)

Thus total revenue will be $11,000

In case of booking of 100 rooms the net revenue in case of 5% cancellations, shall be:

Rooms booked = 100 - 5% = 95

Revenue = 95 [tex]\times[/tex] $150 = $14,250

Less: Variable Costs = 95 [tex]\times[/tex] $30 = ($2,850)

Thus total revenue = $11,400

Since profit in case of booking 100 rooms is more in any case, even in case of least cancellation the revenue will increase.

Thus, this is the optimal number of reservations = 100