$8.$ 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 $$110,$ which is the average room rate. Accommodating an overbooked guest to the nearby resort room is expensive $($average room rate $$180)$ and the inn must pay the room rate difference as its cost to "bump" a customer.

What is the optimal level of overbooking?

Please identify Cu $($under$-$stocking cost$)$ and Co $($over$-$stocking cost$)$ to calculate the critical ratio, i$.$e$.,$ the optimal service level.