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 summer season. An empty room represents an opportunity cost of $69, which is the average room rate. Accommodating an overbooked guest is expensive, however, because the nearby resort rooms average $119 and the inn must pay the difference. What is the optimal level of overbooking? What is the corresponding expected gain per night (as compared to the current policy of no overbooking)? To answer this, assume that the distribution of customers that do not show up is normally distributed with mean 2 and standard deviation 0.5.