Question

Center of Gravity Method: East Texas Seasonings is preparing to build one processing center to serve its four sources of seasonings. The four source locations are at coordinates shown below. Also, the volume from each source is provided. What is the center of gravity? 

	X-coordinate	Y-coordinate	Volume
Athens, Texas	30	30	150
Beaumont, Texas	20	10	350
Carthage, Texas	10	70	100
Denton, Texas	50	50	200

Answer 1

Solution:

The center of gravity coordinates can be calculated as;

X-coordinate = Sum of [Xi x Volume] / Total Volume

Total Volume = 150 + 350 + 100 + 200 = 800

X-coordinate = [(30 x 150) + (20 x 350) + (10 x 100) + (50 x 200)] / 800

X-coordinate = 22,500 / 800

X-coordinate = 28.13

Y-coordinate = Sum of [Yi x Volume] / Total Volume

Y-coordinate = [(30 x 150) + (10 x 350) + (70 x 100) + (50 x 200)] / 800

Y-coordinate = 25,000 / 800

Y-coordinate = 31.25

Center of gravity: X = 28.13, Y = 31.25