Scenario 16.1 - The Stone Lion
The Stone Lion,a bed and breakfast located in a sleepy town,caters to two groups of customers,young couples interested in something marginally more exotic than a staycation,and corporate clients interested in doing some team-building at a location with no cellular service.Corporations know they can get rooms with minimal notice,but young couples on tight budgets tend to plan well in advance of their planned stay at the property.The corporate rate for rooms is $250 per person and the demand pattern is normal with a mean of 20 and a standard deviation of 10.The proprietor of the Stone Lion takes pity on the young couples and charges them only $150 for identical accommodations.
-How many rooms should be reserved for corporate clients?

Question

Quizplus · Accepted Answer

Given the normal distribution of demand for corporate clients (mean = 20, standard deviation = 10), and considering the goal of maximizing revenue while accommodating both corporate clients and young couples, the proprietor should use the concept of overbooking to determine the optimal number of rooms to reserve for corporate clients. The critical fractile formula for newsvendor problems, which balances the cost of overbooking against the cost of underbooking, suggests reserving a number of rooms close to the mean demand when the cost of turning away a customer (opportunity cost) is similar to the cost of an empty room (actual cost). Since the question does not provide specific details on the total number of rooms available or the exact overbooking strategy, the closest answer to the mean demand of 20, without exceeding it, is 17. This choice aims to maximize revenue from the higher-paying corporate clients while leaving some capacity for young couples.

Scenario 16.1 - the Stone Lion