Assignment:
A smaller rural district has the task of locating health posts in the country to serve remove villages. A village is said to be covered, if it is within 10 miles of the health post. The district administration can pay for no more than two health posts. The geographical layout of the villages is shown in Fig., in which the single-digit numbers indicate the distances between the villages, and the double-digit numbers are the populations of the villages:
The covering matrix is then as follows:
(a) Use the Greedy heuristic to locate the two health posts, so as to maximize the benefit of the health posts to the people.
(b) Demonstrate the Swap technique by exchanging the facility that was located first with two other facilities, one at a time. (Choose the facilities with the smallest subscripts). What are the new coverages and would you make either of the swaps permanent?
Provide complete and step by step solution for the question and show calculations and use formulas.