Four hospitals located within a city are cooperating to establish a centralized

Question

Four hospitals located within a city are cooperating to establish a centralized blood-bank facility that will serve the hospitals. The new facility is to be located such that distance traveled is minimized. The hospitals are located as follows: P_1 = (5, 10), P_2 = (7, 6), P_3 = (4, 2), and P_4 = (16, 3). The number of deliveries to be made per year between the blood-bank facility and each hospital is estimated to be 450, 1200, 300, and 1500, respectively. Assuming rectilinear travel, determine the optimum location. What assumption must be made concerning the deliveries of blood? Is it reasonable to expect delivery trips will always be to only one hospital when a delivery is made?

Explanation / Answer

let the optimum location be (x,y)

minimize

Z = 450*sqrt((x-5)^2 + (y-10)^2) + 1200*sqrt((x-7)^2 + (y-6)^2) + 300*sqrt((x-4)^2 + (y-2)^2) + 1500*sqrt((x-16)^2 + (y-3)^2)

solving this in excel we get

x = 7 , y = 6

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