Question 1:
A hypothetical airline operates a flight from point A to point B, with capacity of 50 seats. Typically there are two booking classes on this flight; named T, and Y, where T represents the booking class with the low fare value and Y represents the booking class with the high fare value. Assume also that low fare bookings occur before high fare bookings. Historical observations regarding the number of passengers booked in "Y" class are as shown in the Table below:
|
Number of passengers
|
Number of times this number of passengers was observed
|
Number of passengers
|
Number of times this number of passengers was observed
|
|
0
|
1
|
16
|
31
|
|
1
|
3
|
17
|
30
|
|
2
|
6
|
18
|
27
|
|
3
|
7
|
19
|
26
|
|
4
|
10
|
20
|
25
|
|
5
|
11
|
21
|
21
|
|
6
|
12
|
22
|
19
|
|
7
|
14
|
23
|
14
|
|
8
|
15
|
24
|
13
|
|
9
|
18
|
25
|
11
|
|
10
|
22
|
26
|
10
|
|
11
|
20
|
27
|
7
|
|
12
|
22
|
28
|
4
|
|
13
|
23
|
29
|
3
|
|
14
|
27
|
30
|
2
|
|
15
|
31
|
|
|
a- Enter this data into excel in two columns where the first column represents "Number of passengers" and the second column represents "Number of times this number of passengers was observed". Draw the distribution of the demand values.
b- Using this data,
Calculate the probability that "0" passengers of Y class will show up for this flight
Calculate the probability that exactly 15 passengers show up for this flight
Calculate the probability that at least 15 passengers show up for this flight
Calculate the probability that at most 10 passengers show up for this flight
c- If the fare for "Y" class is $400, calculate the expected marginal seat revenue for each seat of the flight based on the "Y" demand. Put your answer in a table
d- Draw the relation between the seat number (index) and its expected revenue.
e- Based on your calculations, determine the protection level for booking class "Y" in the following cases:
- The fare for passengers of booking class "T" is $100
- The fare for passengers of booking class "T" is $150
- The fare for passengers of booking class "T" is $180