27 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 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.

A B C D E F G H 1 25 5 55 5 35 15 65 45 2 5 25 15 35 25 45 35 55 3 25 55 5 35 35 75 5 35 4 35 15 25 5 55 35 45 25

(a) Which two locations will minimize the total mileage from the trauma centers to the highneed 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.