You are in charge of a new county development. There is a total of 8 regions. Yo
ID: 416403 • Letter: Y
Question
You are in charge of a new county development. There is a total of 8 regions. You are charged with building hospitals to serve all 8 regions. The chart below depicts the city layout.
1
4
7
2
5
8
3
6
Then for example, if a hospital were to be built in Region 1, it would be accessible to Regions 1, 2, and 4. It would not be accessible to diagonal regions, only the ones that are adjoining. Another example, let us suppose that a hospital is built in Region 5, then it would be accessible to Regions 2, 4, 5, 6, and 8.
There is a different cost associated with building a hospital for each region. It would cost $20.5 million, $21.8 million, $16.5 million, $18.2 million, $28.6 million, $23.5 million, $22.4 million, and $19.6 million to build a hospital in Regions 1, 2, 3, 4, 5, 6, 7, and 8, respectively.
What is the minimum cost (in million) incurred for all of the regions to have a hospital accessible to them? For example, if your answer is $25,840,000, you should enter in 25.84
1
4
7
2
5
8
3
6
Explanation / Answer
We would build hospitals in regions 3, 4 and 8.
A hospital built in region 3 would be accessible to regions 2, 3 and 6.
A hospital built in region 4 would be accessible to regions 1, 4, 5 and 7.
A hospital built in region 8 would be accessible to regions 5, 7 and 8.
Thus all the 8 regions are covered with some repetitions of region covered. A minimum of 3 hospitals has to be built to cover all the 8 regions.
Table:
Region for Hospital Location
Cost of building a Hospital (in million $)
3
16.5
4
18.2
8
19.6
Total
54.3
The total cost of building the hospitals in regions 3, 4 and 8 = $ 16.5 million + $ 18.2 million + $ 19.6 million =
$ 54.3 million.
The above total cost would be minimum as the costs of building a hospital in regions 3, 4 and 8 are lowest compared to the costs of building a hospital in the other regions.
Region for Hospital Location
Cost of building a Hospital (in million $)
3
16.5
4
18.2
8
19.6
Total
54.3
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