Question

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. On the grid below, plot the location of the six farm clusters and the calculated mill location. All mileage references use the city of Lake Charles as (0,0). (Show your work)

	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

Answer 1

From the given data,

	dx	dy	W
A	90	10	240000
B	140	60	320000
C	20	70	450000
D	50	20	120000
E	100	80	60000
F	10	120	140000

Now for finding the central location based on center of gravity method,

we have Dx = (d_xA*W_A + d_xB*W_B + d_xC*W_C + d_xD*W_D + d_xE*W_E + d_xF*W_F )/(W_A + W_B + W_C + W_D + W_E + W_F)

and similarly for Dy

thus by putting the values and rounding off we have Dx = 67 and Dy = 58

thus the Central location of the mill would be best at 67 mile East of Lake Charles and 58 miles North of Lake Charles