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). Tonnes KMS east of SC KMS north of SC Moose Jaw 57000 85 16 Regina 41500 135 84 East End 37500 257 91 Estevan 81000 346 12 \begin{array} { | l | r | r | r | } \hline & ext { Tonnes } & ext { KMS east of SC } & ext { KMS north of SC } \\hline ext { Moose Jaw } & 57000 & 85 & 16 \\hline ext { Regina } & 41500 & 135 & 84 \\hline ext { East End } & 37500 & 257 & 91 \\hline ext { Estevan } & 81000 & 346 & 12 \\hline\end{array} Moose Jaw Regina East End Estevan Tonnes 57000 41500 37500 81000 KMS east of SC 85 135 257 346 KMS north of SC 16 84 91 12

Question

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).  Tonnes   KMS east of SC   KMS north of SC   Moose Jaw  57000 85 16  Regina  41500 135 84  East End  37500 257 91  Estevan  81000 346 12 \begin{array} { | l | r | r | r | } \hline  &  	ext { Tonnes }  &  	ext { KMS east of SC }  &  	ext { KMS north of SC } \\hline 	ext { Moose Jaw }  &  57000  &  85  &  16 \\hline 	ext { Regina }  &  41500  &  135  &  84 \\hline 	ext { East End }  &  37500  &  257  &  91 \\hline 	ext { Estevan }  &  81000  &  346  &  12 \\hline\end{array}  Moose Jaw   Regina   East End   Estevan  ​  Tonnes  57000 41500 37500 81000 ​  KMS east of SC  85 135 257 346 ​  KMS north of SC  16 84 91 12 ​ ​

Yarianna Badillo · Accepted Answer

Final Answer :

The centre of gravity, weighted by the tonnage at each village cluster, is about 221.7 KMS east of Speedy Creek and 40.47 KMS north of Speedy Creek.

221.709677440.47235023\begin{array} { | l | r | r | r | } \hline \text { Sum } & 217000 & 823 & 203 \\\hline\text { Average } & 54250 & 205.75 & 50.73 \\\hline \text { Center of Gravity (Wtd Avg) } & & 221.7096774 & 40.47235023 \\\hline\end{array}

$The centre of gravity, weighted by the tonnage at each village cluster, is about 221.7 KMS east of Speedy Creek and 40.47 KMS north of Speedy Creek. \begin{array} { | l | r | r | r | } \hline \text { Sum } & 217000 & 823 & 203 \\ \hline\text { Average } & 54250 & 205.75 & 50.73 \\ \hline \text { Center of Gravity (Wtd Avg) } & & 221.7096774 & 40.47235023 \\ \hline \end{array}$

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