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A golf instructor offers 1-hour private lessons from 2 pm to 6 pm every Saturday afternoon. His hourly rate is $60. The instructor takes appointments during the weekdays. Recently, the instructor receives quite a few late cancellations in Saturday morning. He can do nothing given the short notice. Therefore, the instructor institutes an overbooking policy. In case a customer cannot be served, the instructor will give a $40 certificate (he buys it from the golf club) for a free round of golf. The number of no-shows can be 1, 2, 3, or 4, each with a probability of 0.25. How many reservations should the instructor take

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kaancceylan

Answer:

The answer is 8.

Step-by-step explanation:

He is guaranteed to make $240 between 2 and 6 pm every Saturday afternoon. For each time that both of the 2 customers booked for the same hour does not cancel, he earns only $20. Considering that the probability of cancellation is 25%, if he books 8 customers for the 4 hour period on Saturday afternoon, he is making an extra $80 which bumps up his total earnings to $320. If he accepts any booking after 8, each is going to cost him $40. So the total number of reservations he should take is 8.

I hope this answer helps.

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