Question

[Qs 7-9] Due to increased tourism in Guatemala in the last 10 years, daily flights from La Aurora International Airport, Guatemala City to Tikal National Park have an abundant demand. TAG Airlines has two fare classes (H) High of $300 and a (L) Low fare class of $250. TAG Airlines also overbooks customers to alleviate the costs of no shows. TAG estimates that turning customers away due to overbooking will cost them $350 per customer. Furthermore, they estimate that the distribution of no shows to be Poisson distributed with mean of 3. Each TAG flight has 12 seats.

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

A. 2

B. 3

C. 4

D. Cannot be determined with the information provided.

8. Suppose TAG overbooks 4 passengers (i.e., it takes reservations for 16 passengers), what is the probability that TAG will have to turn customers away?

91.6%

81.5%

64.7%

35.3%

18.5%

8.4%

Cannot be determined from the information provided.

9. 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?

91.6%

81.5%

64.7%

35.3%

18.5%

8.4%

Cannot be determined from the information provided.

Answer 1

Let X be the number of no-shows for a TAG flight X r Poisson(\) where -3 Thus mean number of no shows e-3(3)* n 12 Number of seats in the flight 7) To find maximum number of excess passengers the plane should accept Since the average number of no-shows is 3 for any given flight, the airlines can accommodate on an average 3 passengers without turning them away If the number of excess bookings is more than 3, then the airline might have to turn away atleast 1 passenger on an average Hence maximum number of excess passengers the plane should accept is 3 Answer B. 3 8) Number of passengers overbooked -4 If there are 4 no-shows, then TAG can accommodate these 4 passengers But if there are less than 4 no-shows, TAG will have to turn a few passengers away Thus we find P(X< 4) PlXc4) =P(X 3) -P(x-0) +P(x-1) +P(x-2) + P(x-3) e (3) e3(3)1 (3) e (3) 0! 1! 2! 3! 0.6472 64.7% Answer 64.7% 9) Number of passengers overbooked -3 In this case, there wil be 1 or more empty seats, if there are more than 3 no-shows Thus we find P(X > 3) P(X>3)1- P(X s3) 1 0.6472 - 0.3528 35.3% Answer 35.3%

Answer 2

7 and 8 are wrong