Problem $1(2$ pts$)$ Consider Istanbul$-$London $($single$-$leg$)$ flight with $220$ seats. a$)(1$ pts$)$ The historic show rate has averaged $90\%$ on this flight. What will be the optimal overbooking limit calculated using deterministic heuristic? b$)(1$ pts$)$ Assume that the ticket price is $$300.$ The number x of no$-$shows is independent of total bookings and is given by a normal distribution with mean of $55$ and standard deviation of $12.$ The denied boarding cost is $$400$ per denied boarding. Calculate the optimal booking limit$.$