Four hospitals are located within a city at coordinate points P1 (10, 20), P2 (14, 12), P3 (8, 4), and P4 (32, 6). The hospitals are served by a centralized bloodbank facility that is to be located in the city. The number of deliveries to be made each year between the bloodbank facility and each hospital is estimated to be 450, 1200, 300, and 1500, respectively.

a. If it is desired to locate the bloodbank at a point that minimizes the weighted distance traveled per year, where should it be located if travel is rectilinear in the city?

b. If travel occurs along the tree structure shown below, where should the new facility be located in order to minimize weighted distance traveled?

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25 y-axis 20 20 15 10 5 P = (14,22) P = (26, 18) P3 = (46, 22) P = (36, 10) 0 5 10 15 20 25 30 35 40 40 x-axis 45 50