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 10 250,000
Boudreaux 140 60 300,000
Cancienne 20 70 450,000
Darbonne 50 20 100,000
Evangeline 100 80 50,000
- Calculate the volume-weighted center-of-gravity.
- Calculate the simple center-of-gravity (all cities weighted equally).
- Explain why the two calculations differ.