Hotel manager Basil Fountain and his resourceful assistant,…
Hotel manager Basil Fountain and his resourceful assistant, Casey, run a 26-room hotel in a quaint little town called Poynette. A combination of Mr. Fountain’s friendly attitude and the absence of a respectable inn in the nearby vicinity imply that Mr. Fountain enjoys sufficient demand to fill the hotel at his low fare of $159 per night. Casey notes that some customers will walk into the hotel requesting a room for the night and that they are willing to pay a higher fare of $325 per night. Casey knows that walk-in customer demand varies according to a normal distribution with a mean of 7 and a standard deviation of 2.75. She suggests that some rooms should be held back from the low-fare customers so that they can serve the high-fare customers. To maximize expected profits with Casey’s plan, what is the booking limit that should be set for low-fare customers?
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