A Farmers' Cooperative Association Plans to Build a New Sugar

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).
$\begin{array}{|l|c|c|c|c|}\hline\text { Village } & \text { Miles East of } & \text { Miles North of } & \text { Sugar Cane } \\ & \text { Lake Charles } & \text { Lake Charles } & \text { tonnage } \\\hline \text { Arceneaux } & 90 & 10 & 240,000 \\\hline \text { Boudreaux } & 140 & 60 & 320,000 \\\hline \text { Cancienne } & 20 & 70 & 450,000 \\\hline \text { Darbonne } & 50 & 20 & 120,000 \\\hline \text { Evangeline } & 100 & 80 & 60,000 \\\hline \text { Fontenot } & 10 & 120 & 140,000 \\\hline\end{array}$