A Farmers' Cooperative Association Plans to Build a New Sugar

question 102

Essay

A farmers' cooperative association plans to build a new sugar mill in Southwestern Louisiana. The primary objective of the mill is to provide the farmers with a place to take their crop for processing that will reduce their transportation costs. The members of the co-op believe that the center-of-gravity method is appropriate for this objective. While there are over 200 sugar cane farms in the region, they are tightly clustered around six villages. Using the data below, use the center-of-gravity method to calculate the coordinates of the best location for this mill. On the grid below, plot the location of the six farm clusters and the calculated mill location. All mileage references use the city of Lake Charles as (0,0).
$\begin{array}{|l|c|c|c|c|}\hline\text { Village } & \text { Miles East of } & \text { Miles North of } & \text { Sugar Cane } \\ & \text { Lake Charles } & \text { Lake Charles } & \text { tonnage } \\\hline \text { Arceneaux } & 90 & 10 & 240,000 \\\hline \text { Boudreaux } & 140 & 60 & 320,000 \\\hline \text { Cancienne } & 20 & 70 & 450,000 \\\hline \text { Darbonne } & 50 & 20 & 120,000 \\\hline \text { Evangeline } & 100 & 80 & 60,000 \\\hline \text { Fontenot } & 10 & 120 & 140,000 \\\hline\end{array}$

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Definitions:

Parasympathetic Regulation

The control of body functions by the parasympathetic nervous system, which conserves energy and slows the heart rate, among other functions.

Innervation

The supply of nerves to a specific body part, enabling sensation and movement.

Blood Vessels

Tubular structures carrying blood through the tissues and organs; a network of arteries, veins, and capillaries.

Skeletal Muscles

Voluntary muscles attached to the skeleton that are responsible for movement and maintaining posture by contracting.