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 mew 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 the annual operating cost of no more than $900,000.
the following table shows the coffee shops within 5 minutes’ walking distance of another shop and the average annual cos of the existing stores:
store location
annual average
operating cost ($)
stores within 5 minutes’ walking distance
3rd street
456
3rd street, rose avenue
10th street
207
10th street, south street, broad street
south street
139
south street, hill street, 10th street
mulberry avenue
246
mulberry avenue, beamer boulevard
rose street
177
rose street, 3rd street, church street
wisham avenue
212
wisham avenue, broad street, 23rd avenue
richmond road
195
richmond road, broad street
hill street
170
hill street, south street
23rd avenue
184
23rd avenue, wisham avenue
broad street
163
broad street, wish avenue, richmond road, 10h street
church street
225
church street, rose street, beamer boulevard
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.