A new elementary school is needed in a suburban area of Detroit, Michigan. After extensive research, the school board has narrowed down its choice to three possible sites. The locations for the current residential areas, expected students from each residential area, and possible locations for the school are shown in the tables below.

a. Determine the optimal location for the new elementary school such that the total distance the students have to travel is minimized. It is fair to assume that the construction cost for all three sites is similar and distance is measured rectilinearly.

b. Determine the minimax distance (considering weights, and then ignoring weights).

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Residences x-Coordinate -Coordinate Weight A 20 25 600 B 36 18 400 C 62 37 500 D 50 56 300 E 25 0 200 Possible sites for the new elementary school: Possible Sites x-Coordinate -Coordinate 123 50 50 30 45 3 65 28