Answer to Question #157663 in Statistics and Probability for izzah XV

Question

QUESTION 2

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

400

Answer 1

The center of gravity coordinates can be calculated as

X-coordinate $= \sum\frac{X_i \times Volume }{ Total \;Volume}$

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

X-coordinate $= \frac{(30 \times 150) + (20 \times 350) + (10 \times 100) + (50 \times 200)}{ 800}$

$= \frac{22500 }{ 800} \\ = 28.13$

Y-coordinate $= \sum\frac{Y_i \times Volume }{ Total \; Volume}$

Y-coordinate $= \frac{(30 \times 150) + (10 \times 350) + (70 \times 100) + (50 \times 200) }{ 800}$

$= \frac{25000 }{ 800} \\ = 31.25$

Center of gravity: X = 28.13, Y = 31.25