Mill Mountain Coffee Company currently operates 12 coffee shops in downtown Charlotte. 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 $900,000.
The following table shows the coffee shops within 5 minutes walking distance of another shop and the average annual cost of the existing stores:
|
Store Location
|
Annual Average Operating Cost ($)
|
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
|
|
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.