An important operations decision for service business such as hotels and airlines is the number of reservations to accept to effectively fill canacity knowing that some customers may not use their recervations. If a hotel, for example, holds rooms for customers who do not show up$,$ they lose revenue opportunities. A common practice in these industries is to overbook reservations. When more customers arrive than can be handled, the business usually incurs some cost to satisfy them $($by putting them up at another hotel$).$ A popular resort hotel that has $300$ rooms charges

$$120$

per room per day. Reservations may be canceled by the $6$:$00$ pm deadline with no penalty. The hotel has estimated that the average overbooking cost is

$$100$

$.$ Based on historical data, customer demand can be modeled based on the following discrete distribution: The hotel is willing to accept $310$ reservations; that is$,$ to overbook by $10$ rooms. Also, it is fair to assume that cancellations follow a Poisson Distribution with mean:

$\backslash$lambda $=2$

$.$ The decision becomes how much to overbook to balance the costs of overbooking against the lost revenue for underuse. Therefore, you are required to answer the following questions based on $10,000$ simulations: a$.$ What is the probability that Demand is higher than the Reservation limit of $310?$ b$.$ What is the probability that overbooked customers are greater than $5$ on any day $($Reservation limit is $310)?$ c$.$ What is the Average Net Revenue if the Reservation limit is $310?$ d$.$ Change the Reservation limit of $310$ and use $5$ different values and perform appropriate simulations. Should we change the limit of $310?$ Why?