A farmers' cooperative association plans to build a new grinding mill in Southern Manitoba. 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 a hand drawn grid $($map$),$ plot the location of the four farm clusters and the calculated mill location. All mileage references use the city of Brandon as $(0,0).$

Tonnes KMS east of Brandon KMS south of Brandon

Wawanesa $570005166$

Baldur $4150077102$

Trehern $37500311195$

Glennboro $8100012261$