A hospital in a large city plans to build two satellite trauma centers to provide improved emergency service to areas, such as highways and high-crime districts, that have historically demonstrated an increased need for critical care services. The city council has identified four potential locations for these centers. The table for Problem 6-27 near the top of the next page shows the locations (1-4), and the mileage from each center to each of the eight high-need areas (A-H). Assume that the cost of building the trauma centers will be the same, regardless of which locations are chosen.€ƒ

(a) Which two locations will minimize the total mileage from the trauma centers to the high- need areas? Which locations should be designated to receive injured persons from each of the high-need locations?
(b) Now solve this as a set covering model, assuming that the hospital wants to keep the distance between a high-need location and a trauma center to no more than 35 miles.

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Table for Problem 6-27 25 5 55 5 35 15 65 45 252515 35 25 45 3555 3 25 55 5 35 35 75 5 35 4 35 15 255 55 35 45 25