Question

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 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.

Answer 1

Answer:

The coordinates of the location of the Blood bank = ( 20.7826, 9.73913 )

Explanation:

Coordinates of the Four(4) hospitals are

P1=(10,20),   P2=(14,12),   P3=(8,4) and   P4=(32,6)

Number of deliveries to be made each year for each hospital respectively:

450,   1200,    300, and 1500

conditions :

(i) if travel is rectilinear in the city

(ii) if travel is measured in Euclidean distance.

Determine where the Blood bank is to located to minimize weighted distance travelled each year

find the values of the below variables :

Total load of the Hospitals( ∑load ) = 450 + 1200 + 300 + 1500 = 3450

Lx = ∑x * load = ∑ 10*450 + -------- + 32*1500 = 71700

Ly = ∑y * load = ∑ 20*450 +--------- + 6*1500 = 33600

The coordinates of the Blood bank = [ ( Lx / ( ∑load ) ) ,  Ly /  ( ∑load ) ]

                                                          =[ (71700/3450) , (33600/3450) ]

Hence The coordinates of the  location of the Blood bank = ( 20.7826, 9.73913 )