East Coast Trucking provides service from Boston to Miami us

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

Solution

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 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 and solve an integer linear programming model that can be used to determine the minimum number of service facilities needed and their location.

	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