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?
$$\begin{array} { | l | c | c | c | }
\hline & \text { X-coordinate } & \text { Y-coordinate } & \text { Volume } \
\hline \text { Athens, Texas } & 30 & 30 & 150 \
\hline \text { Beaumont, Texas } & 20 & 10 & 350 \
\hline \text { Carthage, Texas } & 10 & 70 & 100 \
\hline \text { Denton, Texas } & 50 & 50 & 200 \
\hline
\end{array}$$
A) X = 28.125; Y = 31.25
B) X = 22000; Y = 24000
C) X = 27.5; Y = 40
D) center of gravity = 28
E) none of the above

Question

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?
$$\begin{array} { | l | c | c | c | } 
\hline & \text { X-coordinate } & \text { Y-coordinate } & \text { Volume } \
\hline \text { Athens, Texas } & 30 & 30 & 150 \
\hline \text { Beaumont, Texas } & 20 & 10 & 350 \
\hline \text { Carthage, Texas } & 10 & 70 & 100 \
\hline \text { Denton, Texas } & 50 & 50 & 200 \
\hline
\end{array}$$
A) X = 28.125; Y = 31.25
B) X = 22000; Y = 24000
C) X = 27.5; Y = 40
D) center of gravity = 28
E) none of the above

Quizplus · Accepted Answer

The center of gravity is calculated using the formula: $$X = \frac{\sum (Volume \times X-coordinate)}{\sum Volume}$$ and $$Y = \frac{\sum (Volume \times Y-coordinate)}{\sum Volume}$$. Calculating for X and Y gives: $$X = \frac{(150 \times 30) + (350 \times 20) + (100 \times 10) + (200 \times 50)}{150 + 350 + 100 + 200} = 28.125$$ and $$Y = \frac{(150 \times 30) + (350 \times 10) + (100 \times 70) + (200 \times 50)}{150 + 350 + 100 + 200} = 31.25$$.

East Texas Seasonings Is Preparing to Build One Processing Center