East Texas Seasonings Is Preparing to Build One Processing Centre

question 48

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.
$$\begin{array} { | l | l | l | l | } \hline & \text { X-coordinate } & \text { Y-coordinate } & \text { Volume } \\\hline \text { Athens, Texas } & 30 & 40 & 100 \\\hline \text { Beaumont, Texas } & 20 & 15 & 400 \\\hline \text { Carthage, Texas } & 55 & 60 & 150 \\\hline \text { Denton, Texas } & 20 & 70 & 250 \\\hline\end{array}$$

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Definitions:

Fixed Manufacturing Overhead

Costs in manufacturing that do not vary with the level of production output, such as salaries of managers and depreciation of factory equipment.

Machine-Hours

A metric for the amount of time a machine is operational, typically used in manufacturing processes.

Fixed Costs

Costs that do not vary with the level of production or sales over a short period, such as rent, salaries, and insurance.

Estimated Activity

The projected level of activity used to allocate overhead costs, often based on metrics such as machine hours or labor hours.