East Texas Seasonings Is Preparing to Build One Processing Center

Essay

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.
a. Calculate the volume-weighted center of gravity.
b. Calculate the simple center of gravity (all cities weighted equally).
c. Explain why the two calculations differ.
$$\begin{array} { | l | c | c | c | } \hline & \text { X-coordinate } & \text { Y-coordinate } & \text { Volume } \\\hline \text { Athens, Texas } & 30 & 40 & 100 \\\hline \text { Beaumont, Texas } & 20 & 15 & 400 \\\hline \text { Carthage, Texas } & 55 & 60 & 150 \\\hline \text { Denton, Texas } & 20 & 70 & 250 \\\hline\end{array}$$