Mill Mountain Coffee Company currently operates 12 coffee shops in downtown Kelowna. The company has been losing money and wants to downsize by closing some stores. Its policy has been to saturate the downtown area with stores so that one is virtually always in sight of a potential or current customer. However, the company€™s new policy is to have enough stores so that each is within 5 minutes€™ walking distance of another store. The company would also like to have annual operating costs of no more than $900,000. 

The following table shows the coffee shops within 5 minutes walking distance of another shop and the average annual cost of the existing stores.

Formulate and solve a linear programming model that will select the minimum number of stores the company will need to achieve its new policy objective.

Stores Within 5 Minutes' Annual Average Store Location Operating Cost($) Walking Distance 1. 3rd Street 456 3rd Street, Rose Street 10th Street, South Street, Broad 2.10th Street 207 Street 3. South Street 139 South Street, Hill Street, 10th Street 4. Mulberry Avenue 246 Mulberry Avenue, Beamer Boulevard 5. Rose Street 177 Rose Street, 3rd Street, Church Street 6. Wisham Avenue 212 Wisham Avenue, Broad Street 7. Richmond Road 195 Richmond Road, Broad Street 170 8. Hill Street Hill Street, South Street 9. 23rd Avenue 184 23rd Avenue, Wisham Avenue 10. Broad Street 163 Broad Street, Wisham Avenue, Richmond Road, 1Oth Street 11. Church Street 225 Church Street, Rose Street, Beamer Boulevard Beamer Boulevard, Mulberry 12. Beamer 236 Boulevard Avenue, Church Street