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 1 211 320 424 459 565 713 884 1,056 1,196 1,399 1,669 New York 2 109 213 248 354 502 673 845 985 1,188 1,458 Philadelphia 3 104 139 245 393 564 736 876 1,079 1,349 Baltimore 4 35 141 289 460 632 772 975 1,245 Washington 5 106 254 425 597 737 940 1,210 Richmond 6 148 319 491 631 834 1,104 Raleigh 7 171 343 483 686 956 Florence 8
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 1 211 320 424 459 565 713 884 1,056 1,196 1,399 1,669 New York 2 109 213 248 354 502 673 845 985 1,188 1,458 Philadelphia 3 104 139 245 393 564 736 876 1,079 1,349 Baltimore 4 35 141 289 460 632 772 975 1,245 Washington 5 106 254 425 597 737 940 1,210 Richmond 6 148 319 491 631 834 1,104 Raleigh 7 171 343 483 686 956 Florence 8
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 1 | 211 | 320 | 424 | 459 | 565 | 713 | 884 | 1,056 | 1,196 | 1,399 | 1,669 |
| New York 2 | 109 | 213 | 248 | 354 | 502 | 673 | 845 | 985 | 1,188 | 1,458 | |
| Philadelphia 3 | 104 | 139 | 245 | 393 | 564 | 736 | 876 | 1,079 | 1,349 | ||
| Baltimore 4 | 35 | 141 | 289 | 460 | 632 | 772 | 975 | 1,245 | |||
| Washington 5 | 106 | 254 | 425 | 597 | 737 | 940 | 1,210 | ||||
| Richmond 6 | 148 | 319 | 491 | 631 | 834 | 1,104 | |||||
| Raleigh 7 | 171 | 343 | 483 | 686 | 956 | ||||||
| Florence 8 | 172 | 312 | 515 | 785 | |||||||
| Savannah 9 | 140 | 343 | 613 | ||||||||
| Jacksonville 10 | 203 | 473 | |||||||||
| Tampa 11 | 270 | ||||||||||
| Miami 12 |
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
xi
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
x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12 = 0, 1
(b)
Solve the linear program formulated in part (a). How many service facilities are required?
Where should they be located? (Select all that apply.)
BostonNew YorkPhiladelphiaBaltimoreWashingtonRichmondRaleighFlorenceSavannahJacksonvilleTampaMiami
(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
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