East Texas Seasonings is preparing to build one processing centre 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 centre 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) centre of gravity = 24000
E) centre of gravity = 28

Question

East Texas Seasonings is preparing to build one processing centre 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 centre 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) centre of gravity = 24000
E) centre of gravity = 28

Quizplus · Accepted Answer

The center of gravity is calculated using the formula: $$X = \frac{\sum (Volume \times X-coordinate)}{\sum Volume}$$ and $$Y = \frac{\sum (Volume \times Y-coordinate)}{\sum Volume}$$. For X: $$\frac{(150 \times 30) + (350 \times 20) + (100 \times 10) + (200 \times 50)}{150 + 350 + 100 + 200} = \frac{4500 + 7000 + 1000 + 10000}{800} = \frac{22500}{800} = 28.125$$ For Y: $$\frac{(150 \times 30) + (350 \times 10) + (100 \times 70) + (200 \times 50)}{800} = \frac{4500 + 3500 + 7000 + 10000}{800} = \frac{25000}{800} = 31.25$$

East Texas Seasonings Is Preparing to Build One Processing Centre