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, and Tampa. The number of miles between each of the regional offices is provided in the following table:
|
New York
|
Philadelphia
|
Baltimore
|
Washington
|
Richmond
|
Raleigh
|
Florence
|
Savannah
|
Jacksonville
|
Tampa
|
Miami
|
|
Boston
|
211
|
320
|
424
|
459
|
565
|
713
|
884
|
1056
|
1196
|
1399
|
1669
|
|
New York
|
|
109
|
213
|
248
|
354
|
502
|
673
|
845
|
985
|
1188
|
1458
|
|
Philadelphia
|
|
|
104
|
139
|
245
|
393
|
564
|
736
|
876
|
1079
|
1349
|
|
Baltimore
|
|
|
|
35
|
141
|
289
|
460
|
632
|
772
|
975
|
1245
|
|
Washington
|
|
|
|
|
106
|
254
|
425
|
597
|
737
|
940
|
1210
|
|
Richmond
|
|
|
|
|
|
148
|
319
|
491
|
631
|
834
|
1104
|
|
Raleigh
|
|
|
|
|
|
|
171
|
343
|
483
|
686
|
956
|
|
Florence
|
|
|
|
|
|
|
|
172
|
312
|
515
|
785
|
|
Savannah
|
|
|
|
|
|
|
|
|
140
|
343
|
613
|
|
Jacksonville
|
|
|
|
|
|
|
|
|
|
203
|
473
|
|
Tampa
|
|
|
|
|
|
|
|
|
|
|
270
|
The company's expansion plans involve constructing service facilities in some of the cities where a regional office is located. Each regional office must be within 400 miles of a service facility. For instance, if a service facility is constructed in Richmond, it can pro- vide 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 num- ber of service facilities needed and their location.
b. Solve the linear program formulated in part (a). How many service facilities are re- quired, and where should they be located?
c. Suppose that each service facility can only provide service to regional offices within 300 miles. How many service facilities are required, and where should they be located?