1. Let the coordinates be X and Y So we need to minimize the total distances fro

Question

1.

Let the coordinates be X and Y

So we need to minimize the total distances from the current hospitals P1 to P4

So

D1^2 =(X-10)^2 + (Y-20)^2 (no of trips 450)

D2^2 =(X-14)^2 + (Y-12)^2 (no of trips 1200)

D3^2 =(X-8)^2 + (Y-4)^2 (no of trips 300)

D4^2 =(X-32)^2 + (Y-6)^2 (no of trips 1500)

Z= min of ( 450^2* D1^2+1200^2*D2^2+ 300^2* D3^2+ 1500^2*D4^2)

Modifying

Z* = min of 50^2(81*D1^2+ 576*D2^2 + 36*D3^2+ 900*D4^2)

Taking the other factors out

Z**= min of (9 D1^2+ 64*D2^2 + 4*D3^2+ 100*D4^2)

So

Min of (9 D1^2+ 64*D2^2 + 4*D3^2+ 100*D4^2) X component + (9 D1^2+ 64*D2^2 + 4*D3^2+ 100*D4^2) Y component.

For min as all are squares X component will be independently min and Y component will be independently min.

Z1 = min of 177X^2+116100-8346X for X

Z2 = min of 177Y^2+16480-3128Y for Y

So by differentiating for x and y and equating to 0 for minima,

we get

Z1 = 354 X = 8346 , so X = 23.83

Z1 = 354 Y = 3128 , so Y =8.84

Explanation / Answer

Homework 8 TECH 429/529: Plant Layout Location & Mtl. Handling 15 points Due: November 30 2017 . Four hospitals are located within a city at coordinate points Pi (10,20), P (14,12), (8,4) and P4=(32,6). The hospitals are served by a centralized blood bank facility that is 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, and 1500 respectively 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 (i) if travel is rectilinear in the city (ii) if travel is measured in Euclidean distance. (10 points) 2. Six housing subdivisions within a city area are targeted for emergency service by a centralized fire station. Where should the new fire station be located such that the maximum rectilinear travel distance is minimized? The centroid location of the subdivision are as follows: (5 points) Subdivision x-coordinate 20 25 13 25 rdinate 15 25 32 14 21 18

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