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A family-run inn has 50 rooms. The inn is considering the use of overbooking, because the frequency of no-shows has left many rooms vacant during

A family-run inn has 50 rooms. The inn is considering the use of overbooking, because the frequency of no-shows has left many rooms vacant during the past summer season. Based on the past experience, the number of no-shows is an approximated normal distribution with a mean of 3 and a standard deviation of 4. The average room rate of the inn is $60/night. The inn's average cost of operating a room is $28/night, no matter it is empty or occupied. Accommodating an overbooked guest is expensive. The inn must book a room with one of the two nearby resorts for the overbooked guest, and pay the difference. Rooms in resort A have an average price of $123/night. The room availability in resort A is 26%. The average room rate of resort B is $156/night. There is always room available in resort B, i.e., the probability of room availability is 100% for resort B.

What would be the cost Cu if the inn under-estimates the number of no-shows?

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