Nine hospitals are located within a city at coordinate points P1 (10, 20), P2 (14,12), P3(8, 4) , P4 (32, 6), P5 (9,16), P6 (20,30), P7 (15,5), P8 (5,10), P9 (30,7) . The hospitals are served by a centralized blood bank facility that is to be located in the city The number of deliveries to be made each year between the blood bank facility and each hospital is estimated to be 450 1200 300, 1500,250,400, 600, 100,500 respectively.

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

(b) What other method can you apply to validate your previous solution in (a)? (Ensure sufficient proof/ evidence of the method is presented such as a screenshot PDF/calculations etc)

(c) Where should the blood bank facility be located if it is desired that the Euclidean minimum problem be solved to locate the blood bank?