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, apply the center-of-gravity method to calculate the coordinates of the best location for this mill. All mileage references use the city of Lake Charles as (0,0). Miles East of Miles North of Village Arceneaux Lake Charles Lake Charles Sugar Cane tonnage 90 Boudreaux 140 60 Cancienne 20 Darbonne 50 Evangeline 100 Fontenot 10 282282 10 240,000 320,000 70 450,000 20 120,000 80 120 60,000 140,000