Question

Collection Point Weight X coord Y coord
A 9,000 4 8
B 4,000 7 2
C 2,000 4 1
D 5,000 7 3
Sum 20,000 22 14
Average 5.5 3.5
Weighted Average 5.35 4.85

13) A manufacturer of stamped metal auto parts has four parts factories in one city at the location coordinates shown below. Each coordinate unit represents a city block (roughly 100 meters). The yearly demand at each factory is also given.


Factories Demand X-Coord. Y-Coord.
Rayburn Industrial Park 19,000 20 130
Port of Zavalla 3,000 60 40
Henderson Mfg.Center 5,000 70 100
Wax Mills Site 6,000 90 30

Management has decided to build a new sheet metal mill, to supply these factories, at a location central to these plants. What should be the map coordinates of the new plant? On the grid below, graph the locations of the four parts factories and the proposed sheet metal mill.

Answer: The mill should be located near (44, 99). The center-of-gravity model does not favor any single data point; it is the weighted average of them all. In this case, being central does not mean being close to any single factory, but it is closer to the collection of all four than any other mill location could be.

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