Chapter 10: Question 3 Given the following information, determine the optimal overbooking policy for Talia's 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 goodwill per patron due to overbooking is approximately $50. Formula: Expected net profit = (profit - turnaway cost) * no-show probability No Shows Probability Patrons 0 0.50 8 9 10 1 0.30 8 9 2 0.20 6 7 8 Expected Profit with 8 Patrons No Shows 0 1 Patrons 8 6 Profit 800 700 600 Turn-away 0 0 0 Cost 0 0 0 Net Profit 800 700 600 Probability 0.50 0.30 0.20 Expected Profit 400 210 120 Total Expected Profit $730 Expected Profit with 9 Patrons No Shows 0 2 Patrons 700 Profit 900 800 700 Turn-away 0 0 Cost 50 0 0 Net Profit 850 800 700 Probability 0.50 0.30 0.20 Expected Profit 425 240 140 Total Expected Profit $805