4. [30 points] A heavy equipment manufacturer wants to find locations of its spare part regional distribution centers. The customers value faster delivery of spare parts to their locations than the costs. Therefore, the equipment manufacturer wants to locate its spare parts distribution centers within 1000 miles of customer locations. Assume that the cost of establishing a spare parts distribution center at any location is equal. The table below shows the distances between customer locations and potential spare parts distribution center locations. (Refer the presentation for the description of location codes) DC locations Customer Locations Distance (miles) AT BO CH DE HO LA NO NY PI SL SF SE AT 0 1037 674 1398 789 2182 479 841 687 1878 2496 2618 CH 674 1005 0 1008 1067 2054 912 802 452 1390 2142 2013 DE 1398 1949 1008 0 1019 1059 1273 1771 1411 504 1235 1307 LA 2182 2979 2054 1059 1538 0 1883 2786 2426 715 379 1131 NY 841 222 802 1771 1608 2786 1311 0 368 2182 2934 2815 SF 2496 3095 2142 1235 1912 379 2249 2934 2578 752 0 808 SE 2618 2976 2013 1307 2274 1131 2574 2815 2465 836 808 0 a. Which distribution centers should be established? How many distribution centers are required in total? b. If the cost of establishing a distribution center (in millions of dollars) for the locations are given in the table below. Which distribution centers should be established now? Is it different from the answer in (a)? AT CH DE LA NY SL SF 80 75 80 90 100 150 60 SHOW EXCEL STEPS N WORK