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 $$110,$ which is the average room rate. Accommodating an overbooked guest is expensive, however, because the nearby resort rooms average $$180$ and the inn must pay the difference as its cost to "bump" a customer.

What is the optimal level of overbooking?