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 All mileage references use the city of lake charles as (0,0). Village miles east of Lake Charles miles north of Lake Charles sugar cane tonnage arceneaux 90 10 240,000 boudreaux 140 60320,000 cancienne 20 70 450,000 darbonne 50 20 120,000 evangeline 100 80 60,000 fontenot 10 120 140,000