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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

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

60

320,000

Cancienne

20

70

450,000

Darbonne

50

20

120,000

Evangeline

100

80

60,000

Fontenot

10

120

140,000

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