The following table gives the map coordinates and the shipping loads for a set o

Question

The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub.

City Shipping Load Map Coordinates (x) Map Coordinates (y)

A 5 4 10

B 11 7 7

C 14 4 7

D 4 7 4

E 15 6 8

F 9 4 2

G 4 3 7

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A.) For the location of the proposed new central hub, the coordinates should be near : (round 2 decimal places)

x=

y=

B.) If the shipments from city A double for the location of the proposed new hub, the coordinates should be near : (round 2 decimal places)

x=

y=

Explanation / Answer

A) The coordinates of the proposed new central hub are determined using the center of gravity method

X coordinate of proposed new central hub = Xi*Si/Si,   (where Xi is the X coordinate of city i and Si is the shipping load of city i )

= (5*4+11*7+14*4+4*7+15*6+9*4+4*3)/(5+11+14+4+15+9+4) = 5.15

Y coordinate of proposed new central hub = Yi*Si/Si,   (where Yi is the Y coordinate of city i and Si is the shipping load of city i )

= (5*10+11*7+14*7+4*4+15*8+9*2+4*7)/(5+11+14+4+15+9+4) = 6.56

X = 5.15

Y = 6.56

B) The new shipment from city A = 2*5 = 10

X coordinate of proposed new central hub = Xi*Si/Si

= (10*4+11*7+14*4+4*7+15*6+9*4+4*3)/(10+11+14+4+15+9+4) = 5.06

Y coordinate of proposed new central hub = Yi*Si/Si

= (10*10+11*7+14*7+4*4+15*8+9*2+4*7)/(10+11+14+4+15+9+4) = 6.82

X = 5.06

Y = 6.82

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