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 = $150 100 = $15,000
Less: Overbooked charges = $200 5 = ($1,000)
Less: Variable Cost = $30 100 = ($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 $150 = $14,250
Less: Variable Costs = 95 $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