A family-run inn is considering the use of overbooking because the frequency of no-shows listed below has left many rooms vacant during the past 100 days An empty room represents an opportunity cost of $100, which is the average room rate. Assume no-shows are not penalized (or in other words, the payment happens upon completion of the service) Accommodating an overbooked guest is expensive, because the nearby resort rooms average $150 and the inn must pay the difference to the customer. (read carefully!) The number of no-shows is our variable. The number of overbookings is our variable. Approach 1: Calculate Expected Loss Hint: the expected loss for not overbooking at all =0.50+0.1100+0.15200+0.15300+0.1400 ) - The expected loss of not overbooking at all (i.e., X=0 ) is - The expected loss of overbooking only 1 room \$ - The expected loss of overbooking 2 rooms $ - The expected loss of overbooking 3 rooms $ - The expected loss of overbooking 4 rooms - The optimal number of overbooking (X) is rooms, because it minimizes the expected loss Approach 2: Calculate Critical fractile - The overage cost (i.e., lost revenue due to many overbookings) is $ - The underage cost (i.e., lost revenue due to not enough overbookings) is $ - The critical fractile value is - The optimal number of overbookings (X) is the highest X that satisfies this Pr(D