Suppose a new hospital is to be built to provide medical and healthcare service

Question

Suppose a new hospital is to be built to provide medical and healthcare service to 5 towns coordinate (5,6), (1,3), (13,7),(11,2) and (8,1) on map, the transportaion network is rectilinear travel

1. Determine the corordinates of potetial site for hospital to be built so that distnace of hosptal to furthest town is minimize. State any assumption used

2. if it is not possible to build hospital at site that have x coordinates less than 7 and a new hospital is to be built on site recommended from (i) which town would be furthest away from hosptial and what is the distance

Explanation / Answer

1.centre point= x axis=(5+1+13+11+8)/5=38/5=7.6

y axis=(6+3+7+2+1)/5=19/5=3.8

if hospital has to be build in only intiger cordinates and can be built any where then ideal place is centre point (8,4)

nearest point to center is (8,1)

if it has to be buil in one among the above places then calculating farthest points from each point

(5,6)

(1,3) farthest point(13,7)=|12,4|=12.64

(13,7) farhest point (1,3)=12.64

(11,2) farthest point (1,3)=(10,1)=10.04

(8,1) farthest point (13,7) =|5,6|=7.8

the pont which has min distance to fartest point is (8,1)

2)if x>7

(8,1) is place for hospitha with (13,7) at farthest distance 7.8units

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