Twobucks Coffee Company currently operates 12 coffee shops in downtown Nashville. 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 the 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:

Store Location Annual Average Operating Cost ($) Stores Within 5 Minutes’ Walking Distance 1. 3rd Street 456 3rd Street, Rose Street 2. 10th Street 207 10th Street, South Street, Broad 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, 23rd Avenue 7. Richmond Road 195 Richmond Road, Broad Street 8. Hill Street 170 Hill Street, South Street 9. 23rd Avenue 184 23rd Avenue, Wisham Avenue 10. Broad Street 163 Broad Street, Wisham Avenue, Richmond Road, 10th Street 11. Church Street 225 Church Street, Rose Street, Beamer Boulevard 12. Beamer Boulevard 236 Beamer Boulevard, Mulberry Avenue, Church Street 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.

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