East Cost Trucking provides specialized shipping services in major cities along the east cost of the United States. The company currently has facilities in Boston, New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, Florence, Savanna, Jacksonville, and Tampa. The company wants to expand it service offerings by purchasing new trucks for some of the regional facilities. The trucks are larger and more fuel efficient than what the company is currently using. Management realizes that they cannot afford to purchase a new truck for each regional facility. The company has also decided that no more than one new truck will be purchased for a regional city. In other words, a single new truck will be purchased for a given facility or it will not. However, if a truck is purchased for a facility, it can service other cites as long as the other cities they are located no more than 400 miles away. For example, if a truck is purchased and placed in Richmond, it can provide service to itself and New York, Philadelphia, Baltimore, Washington, Raleigh, and Florence, because each city is located within 400 miles from Richmond. 

The company wants to determine the minimum number of trucks that they have to purchase if every city is to be serviced by at least one new truck. Therefore, the company not only needs to know the minimum number of trucks to purchase, they need to know which facilities will receive the new trucks so that all other cities are serviced by at least one new truck.
The number of miles between the regional facilities is provided in the following table.

Formulate a binary program that can be used to determine the minimum number of trucks that are needed and their locations.

Savual Phiadelphie 320 109 Bultimore Weshingiun 459 Sustun New Turk Kkhumond slurene Jucksumile Miami Boston 211 424 1669 565 354 713 884 1196 985 1.399 New Yor 211 213 248 502 673 645 1.188 Phiarielphin 120 104 745 1,070 Bakimure 424 213 104 141 772 2,245 Wuhingtuas 24 199 940 Richmond 565 354 245 141 106 145 319 491 631 834 Raleigh 713 502 393 299 254 148 171 343 483 Finrence 475 171 177 Savannah 343 341 atksunvil 205 272 12 140 201 478 Tampa LI 1,079 975 515 143 203 273 Miami 1349 L24 1210 LI04 785 GLD 473 270