Due to increased tourism in Guatemala in the last 10 years, TAG Airlines operates daily flights from La Aurora International Airport, Guatemala City to Tikal National Park. TAG Airlines has two fare classes: a High fare class (H) of $300 and a Low fare class (L) of $250. Customers for the low fare buy their tickets well in advance, whereas high fare customers show up on the day of the flight. Furthermore, there is ample demand for the low fare class, but the high fare demand is random. TAG Airlines also overbook customers to alleviate the costs of no shows. TAG estimates that turning customers away due to overbooking will cost them $350 per customer (which includes the cost of refunding the ticket). Furthermore, they estimate the distribution of no shows to be Poisson distributed with a mean of 3. Each TAG flight has 12 seats.

A. What is the maximum number of excess passenger reservations the plane should accept?

B. Suppose TAG overbooks 4 passengers (i.e., it takes reservations for 16 passengers). What is the probability that TAG will have to turn one or more customers away?

C. Suppose TAG overbooks 3 passengers (i.e., it takes reservations for 15 passengers). What is the probability that TAG will have one or more empty seats on its flight?

D. Suppose TAG overbooks 2 passengers (i.e., it takes reservations for 14 passengers). What is the probability that TAG will have three or fewer empty seats on its flight?

E. Suppose TAG overbooks 2 passengers (i.e., it takes reservations for 14 passengers). What is the probability that TAG will have to turn away three or more customers on its flight?