Chapter 8-Location Planning Center of Gravity Method When quantities shipping to

Question

Chapter 8-Location Planning Center of Gravity Method When quantities shipping to all locations are equal X Coordinate 20 30 50 80 Y Coordinate 20 50 40 50 Quantity (units) 10 10 10 10 Destination 1. Find the coordinate for the x-axis. [45] 2. Find the coordinate for the y-axis. [40] When quantities shipping to locations are different: X Coordinate 20 30 50 80 Y Coordinate 20 50 40 50 Quantity (units) 5,000 5,000 4,000 6,000 Destination 1. Find the coordinate for the x-axis. [46.5] 2. Find the coordinate for the y-axis. [40.5]

Explanation / Answer

When quantities shipping to all locations are equal

Coordinate for the X axis

= Sum of X values of 4 destinations/ 4 i.e number of destinations

= ( 20 + 30 + 50 + 80 ) / 4

= 180 /4

= 45

Coordinate for the Y axis

= sum of values of 4 destinations / 4 i.e. number of destinations

= ( 20 + 50 + 40 + 50 ) / 4

= 160/4

= 40

When quantities shipping to all locations are equal :

( Sum of all quantities) x Coordinate of X axis = Sum ( Quantity x Corresponding X coordinate)

Or, ( 5000 + 5000 + 4000 + 6000).X

= 5000 X 20 + 5000 X 30 + 4000 X 50 + 6000 X 80

Or , 20000.X = 100000 + 150000 + 200000 + 480000

Or, 20000.X = 930000

Or, X = 930000/20000

Or, X = 46.5

( Sum of all quantities) x Coordinate of X axis = Sum ( Quantity x Corresponding Y coordinate)

Or, ( 5000 + 5000 + 4000 + 6000).Y = 5000 x 20 + 50 x 5000 + 40 x 5000 + 50 x 5000

Or, 20000.Y = 100000 + 250000 + 200000 + 250000

Or, 20000.Y = 800000

Or, Y = 800000/20000

Or, Y = 40

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