A Farmers' Cooperative Association Plans to Build a New Grinding

Essay

A farmers' cooperative association plans to build a new grinding mill in Southern Saskatchewan. 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 centre-of-gravity method is appropriate for this objective. While there are over 200 wheat farms in the region, they are tightly clustered around four villages. Using the data below, use the centre-of-gravity method to calculate the coordinates of the best location for this mill. On the grid below, plot the location of the four farm clusters and the calculated mill location. All mileage references use the city of Speedy Creek as (0,0).
$$\begin{array} { | l | r | r | r | } \hline & \text { Tonnes } & \text { KMS east of SC } & \text { KMS north of SC } \\\hline \text { Moose Jaw } & 57000 & 85 & 16 \\\hline \text { Regina } & 41500 & 135 & 84 \\\hline \text { East End } & 37500 & 257 & 91 \\\hline \text { Estevan } & 81000 & 346 & 12 \\\hline\end{array}$$