East Texas Seasonings Is Preparing to Build One Processing Centre

Essay

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