The following table gives the map coordinates and the shipping loads for a set o
ID: 342793 • Letter: T
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 Shipping Load Map Coordinates (x,y) (5,10) (5,8) (5,9) (8,6) (6,9) (2,3) City 15 9 a) For the location of the proposed new central hub, the coordinates should be near: (round your response to two decimal places) (round your response to two decimal places) b) If the shipments from city A triple, for the location of the proposed new central hub, the coordinates should be near: (round your response to two decimal places) (round your response to two decimal places)Explanation / Answer
The problem will be solved using Center of gravity method.
Accordingly,
Sum of all shipping loads x P = Sum of ( X coordinate x Shipping load ) for 7 cities
Or, ( 5+11+16+6+15+9+6 ).P = 5x5 +5x11+5x16+8x6+6x15 +2x9 + 1x6
Or, 68.P = 25 + 55 + 80 + 48 + 90 + 18 + 6
Or, P = 322/68
Or, P = 4.73
Sum of all shipping loads x Q = Sum of ( Y coordinate x Shipping load ) for 7 cities
Or, ( 5 + 11 + 16 + 6 + 15 + 9 + 6 ).Q = 5X10 + 11X8 +16X9 +6X6 + 15X9 + 9X3 +6X6
Or, 68 .Q = 50 + 88 + 144 + 36 + 135 + 27 + 36
Or, Q = 516/68
Or, Q = 7.59
X = 4.73
Y = 7.59
Let the coordinate of the center of gravity i.e. the central hub = P11, Q1
Accordingly,
Sum of all shipping loads x P = Sum of ( X coordinate x Shipping load ) for 7 cities
Or, ( 15+11+16+6+15+9+6 ).P = 15x5 +5x11+5x16+8x6+6x15 +2x9 + 1x6
Or, 78.P = 75 + 55 + 80 + 48 + 90 + 18 + 6
Or, P = 372/78
Or, P = 4.77
Sum of all shipping loads x Q = Sum of ( Y coordinate x Shipping load ) for 7 cities
Or, ( 15 + 11 + 16 + 6 + 15 + 9 + 6 ).Q = 15X10 + 11X8 +16X9 +6X6 + 15X9 + 9X3 +6X6
Or, 78 .Q = 150 + 88 + 144 + 36 + 135 + 27 + 36
Or, Q = 616/78
Or, Q = 7.90
X = 4.77
Y = 7.90
X = 4.73
Y = 7.59
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