How hard is it to expand a set-covering model to accommodate new cities? Answer this by modifying the model in Figure 14.55. Add several cities that must be served: Memphis, Dallas, Tucson, Philadelphia, Cleveland, and Buffalo. You can look up the distances from these cities to each other and to the other cities in a reference book (or on the Web), or you can make up approximate distances.
a. Modify the model appropriately, assuming that these new cities must be covered and are candidates for hub locations.
b. Modify the model appropriately, assuming that these new cities must be covered but are not candidates for hub locations.

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Figure 14.55 Modified Hub Location Model D K. M 1 Western Airlines hub location model with distances 3 Input data 4 Mile limit Range names used: Hubs covered_by -Modell SES43:SBSS4 Total hubs Used as_hub? Modell$8S57 Modell$8S39:$MS39 1000 6 Distance from each city to each other city BO O 1037 DE HO NY 687 1878 2496 2618 7. AT CH LA 789 2182 NO SL SF SE 8 JAT 674 1398 479 841 9 BO 10 CH 11 DE 12 HO 13 LA 14 NO 15 INY 1037 1005 1949 1804 2979 1507 222 574 2343 3095 2976 674 1005 O 1008 1067 2054 912 802 452 1390 2142 2013 1398 1949 O 1019 1059 1273 17711 1411 O 1538 O 1883 2786 2426 715 1008 504 1235 1307 789 1804 1067 1019 356 1608 1313 1438 1912 2274 2182 2979 2054 1059 1538 379 1131 479 1507 912 1273 356 1883 O 1311 1070 1738 2249 2574 841 222 802 1771 1608 2786 1311 368 2182 2934 2815 16 PI 687 574 452 1411 1313 2426 1070 368 O 1826 2578 2465 17 SL 18 SF 19 SE 1878 2343 1390 504 1438 715 1738 2182 1826 752 836 2496 3095 2142 1235 1912 379 2249 2934 2578 752 808 2618 2976 2013 1307 2274 1131 2574 2815 2465 836 808 20 21 Which dities are covered by which potential hubs with this mile limit 22 23 City 24 AT 25 B0 26 CH Potential hub AT BO CH DE HO LA NO NY PI SL SF SE 1 1 이 of 1 1 1 27 DE 28 HO 29 LA 1 1 1 30 NO 31 NY 32 PI 33 SL 34 SF 35 SE 36 37 Dedsions: which dties to use as hubs 38 1 1 of 1 1 1 1 1 1 1 1 ol 1 AT BO CH DE но LA NO NY PI SL SF SE 39 Used as hub? 40 41 Constraints that each city must be covered by at least one hub 42 City 43 AT 44 Bo 1 Hubs covered by Required 2 45 CH 1 1 46 DE 47 HO 48 LA 49 NO 50 NY 1 1 1 1 1 1 1 1 51 PI 1 52 SL 53 SF 54 SE 1 Note: There are multiple optimal solutions to these problems, so don't be surprised if you don't get exactly the same hub locations as shown here. 55 56 Objective to minimize 57 Total hubs