Given the following information, determine the optimal overbooking policy for a beauty salon. The salon€™s capacity is 8 patrons. The historic number of no-shows for a typical day along with the probability of occurrence is shown in the table. The average profitability per patron is $100 and the cost of lost good-will per patron due to overbooking is approximately $50.

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Reservations/Showing Up No-Shows Probability 8 9. 10 0.50 10 0.30 0.20 6 2.