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.

No-Shows Probability

0 0.50

1 0.30

2 0.20