Mr Smith and his family were planning a vacation. They wished to have a trip tha

Question

Mr Smith and his family were planning a vacation. They wished to have a trip that had an activity at a water park, spa, a golf course, and also exploring local food. By searching through travelling promotions, there were only four city tours (Singapore, Bali, Bangkok, and Hawaii) that they really wanted to go. The key features are as follow.

(1) Both Hawaii and Singapore tours were featured with a great water park experience.

(2) Both Bali and Bangkok tours were featured with the best spa in the city.

(3) The Hawaii and Bali tours included one day for playing golf.

(4) Bangkok tour included one day authentic Thai food tour. Unfortunately, none of the four city tours included all four activities that they wanted. Moreover, every pair of the six possible activity pairs was met by only one city tour. For example, only the Bangkok tour had a pair of spa and food. Mr Smith had to choose the tour that met the most of the preferences.

Which tour did he choose?What assuptions do we need to solve this problem?

Explanation / Answer

Hawaii: water park, golf

Singapore: water park

Bali: Spa, Golf

Bangkok: Spa, food tour

From the above set, Singapore can be removed from the list because it meets only one preference.

To make a choice out of the three remaining cities, we need to know what preference order Mr Smith has assigned to each of these four activities.

For example:

If Mr Smith's preferences are in this order:

1 water park

2 local food

3 spa

4 golf course

Then, the preference marks for the remaining three cities are:

Hawaii: water park, golf: 1+4 = 5

Bali: Spa, Golf: 3+4 = 7

Bangkok: Spa, food tour = 2+3 = 5

The city with the lowest preference marks has the highest priority. In this case, we have a tie between, Hawaii and Bangkok. However, Hawaii covers the most preferred and the least preferred activities, whereas Bangkok covers the middle two activities. Thus, Mr Smith will chose Bangkok as his city for tour.

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