A long-distance bus company offers a standard tickets to travel between Hamburg and Munich for a price of 100,-- . The company only has standard buses offering seats for 60 passengers.

Based on the last 80 journeys the company documented the following no show figures of passengers having bought tickets. Data is used for decision making by senior management:

There is no differentiation in ticket classes by the bus company.

a) Please describe the planning problem of the bus company.

b) Please estimate the probability that there are 10 (or more) no-show passengers of the respective trip.

A passenger having bought a ticket who cannot be seated in the bus must be compensated by

- refunding the ticket price paid and

- an airline ticket (to be purchased by the company for a price of 300,-- )

c) Please argue whether it is favourable to sell more tickets (than seats available) and determine the respective number of overbooked seats.

No shows Frequency Cum frequency OUT O 0 5 5 1 6 11 10) 2 3 4 5 8 1 5 6 19 20 25 31 00 N ] 6 8 39 O 12 7 8 9 8 76 47 5460 10 11 51 65 66 12 13 14 2 3 4 68 71 75 3 15 16 17 18 19 2 1 1 1 0 77 78 79 80 80 20 0 80 8 12 + No shows Frequency Cum frequency OUT O 0 5 5 1 6 11 10) 2 3 4 5 8 1 5 6 19 20 25 31 00 N ] 6 8 39 O 12 7 8 9 8 76 47 5460 10 11 51 65 66 12 13 14 2 3 4 68 71 75 3 15 16 17 18 19 2 1 1 1 0 77 78 79 80 80 20 0 80 8 12 +