(Solved): East Coast Trucking provides service from Boston to Miami using regional offices located in Boston ...

East Coast Trucking provides service from Boston to Miami using regional offices located in Boston, New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, Florence, Savannah, Jacksonville, Tampa, and Miami. The number of miles between each of the regional offices and the numbers associated with each city are provided in the following table. New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami Boston New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami 1 12 3 4 5 6 7 8 9 1 1 11 211 320 109 424 213 104 459 248 139 35 565 354 245 141 106 713 502 393 289 254 148 884 673 564 460 425 319 171 1,056 845 736 632 597 491 343 172 1,196 985 876 772 737 631 483 312 140 1,399 1,669 1,188 1,079 975 940 834 686 515 343 203 1,458 1,349 1,245 1,210 1,104 956 785 613 473 270 The company's expansion plans involve constructing service facilities in some of the cities where a regional office is located, such that each regional office is within 400 miles of at least one service facility. For instance, if a service facility is constructed in Richmond, it can provide service to regional offices located in New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, and Florence. Management would like to determine the minimum number of service facilities needed and where they should be located. (a) Formulate an integer linear program that can be used to determine the minimum number of service facilities needed and their location. (Let x; be the 0-1 variable, which is 1 if a service facility is constructed in city i, and 0 otherwise.) (a) Formulate an integer linear program that can be used to determine the minimum number of service facilities needed and their location. (Let x; be the 0-1 variable, which is 1 if a service facility is constructed in city i, and 0 otherwise.) Min s.t. Boston New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami X31X41X51X61X7 X8 X9 X10 X11 X12 = 0, 1 (b) Solve the linear program formulated in part (a). How many service facilities are required? (b) Solve the linear program formulated in part (a). How many service facilities are required? Where should they be located? (Select all that apply.) Boston New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami (c) Suppose that each service facility can only provide service to regional offices within 300 miles. How many service facilities are required? Where should they be located? (Select all that apply.) Boston New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami