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  • A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with The flight durati

A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with The flight duration between any pair of cities will be less than one hour To start operations, the company has to decide on a daily schedule.


The underlying principle that they are working on is the following:


Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day

Question : Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and/or terminating in one of the hubs Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is:

Option: 1

54


Option: 2

120


Option: 3

96


Option: 4

60


Answers (1)

best_answer

The underlying principle of the airline is that any person staying in any of the 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day. This means that there must be at least one morning flight and one evening flight between any pair of cities.

If three of the ten cities are to be developed as hubs, then each of these hubs will be connected with every other city by direct flights each way, both in the morning as well as in the evening. This means that there will be a total of  4\times7=28  direct flights originating or terminating at each hub. For all three hubs, this will total  28\times3=84 direct flights.

In addition to this, the three hubs must be connected amongst themselves. Since there must be four flights between any pair of cities, there must be a total of  4\times3=12 flights connecting any pair of hubs.

Therefore, the minimum number of direct flights that need to be scheduled to satisfy the underlying principle is 84 + 12 = 96.

 

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Nehul

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