### Problem Solving with Linear Programming #### Task (b) **Objective**: Solve the linear program formulated in part (a). Determine how many service facilities are required. **Input Required**: - Input the number of service facilities in the provided box. **Location Options**: Select all applicable locations for the service facilities from the following list: - Boston - New York - Philadelphia - Baltimore - Washington - Richmond - Raleigh - Florence - Savannah - Jacksonville - Tampa - Miami --- #### Task (c) **Objective**: Assume each service facility can only provide service to regional offices within 300 miles. Determine how many service facilities are required under these conditions. **Input Required**: - Input the number of service facilities in the provided box. **Location Options**: Select all applicable locations for the service facilities from the following list: - Boston - New York - Philadelphia - Baltimore - Washington - Richmond - Raleigh - Florence - Savannah - Jacksonville - Tampa - Miami This exercise helps in understanding the application of linear programming in optimizing the location of service facilities based on geographical constraints. It emphasizes decision-making regarding facility numbers and locations for efficient operation within specific limitations. **East Coast Trucking Regional Office Distances** East Coast Trucking provides service along the East Coast from Boston to Miami. The company utilizes regional offices located in the following cities: Boston, New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, Florence, Savannah, Jacksonville, Tampa, and Miami. The table below shows the number of miles between each of these regional offices. | | New York | Philadelphia | Baltimore | Washington | Richmond | Raleigh | Florence | Savannah | Jacksonville | Tampa | Miami | |----------------|----------|--------------|-----------|------------|----------|---------|----------|----------|--------------|-------|-------| | **Boston** | 211 | 320 | 424 | 459 | 565 | 773 | 884 | 1,056 | 1,196 | 1,399 | 1,669 | | **New York** | | 109 | 213 | 248 | 354 | 502 | 673 | 845 | 985 | 1,188 | 1,458 | | **Philadelphia** | | | 104 | 139 | 245 | 393 | 564 | 736 | 876 | 1,079 | 1,349 | | **Baltimore** | | | | 35 | 141 | 289 | 460 | 632 | 772 | 975 | 1,245 | | **Washington** | | | | | 106 | 254 | 425 | 597 | 737 | 940 | 1,210 | | **Richmond** | | | | | | 148 | 319 | 491 | 631 | 834 | 1,104 | | **Raleigh** | | | | | | | 171 | 343 | 483 | 686 | 956 | | **Florence** | | | | | | | | 172 | 312 | 515 | 785 | | **Savannah** | | |