Walmark Stores is in in the process of expansion in the western United States. During the next year,

Walmark is planning to construct new stores that will serve 10 geographically dispersed communities. Past experience indicates that a store must be within 25 miles of a community to attract customers. In addition, the population of a community plays an important role in where a store is located, in the sense that bigger communities generate more participating customers. The following table provides the populations as well as the distance in miles between the communities:

(a) How many stores are needed in order to capture the whole population?

(b) If Walmark can built a maximum of 4 stores, where should they be located to maximize the number of customers attracted?

Assume that customers will go to a Walmark store regardless of how far away it’s located, where should Walmark build its stores if it wants to

(c) minimize the average distance a customer must travel to visit a store.

(d) minimize the maximum distance a customer must travel to visit a store.

Miles from community i to communityj 2 3 20 40 35 6. 8. 9 10 Population 10,000 17 24 50 58 33 12 2 20 23 68 40 30 20 36 70 22 45 70 19 70 40 15,000 3 40 23 30 21 80 28.000 4. 35 68 36 80 24 20 40 10 30.000 17 70 70 23 70 13 40 14 50 50 40 40 40,000 30,000 20,000 6. 24 30 22 80 23 12 50 20 45 24 70 12 26 40 30 14 26 20 50 20 22 50 22 8 58 19 30 20 40 15,000 60,000 33 70 21 40 13 50 40 10 12 40 80 10 40 50 30 12.000