A farmers\' cooperative association plans to build a new sugar mill in Southwest
ID: 335846 • Letter: A
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
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
Explanation / Answer
From the given data,
Now for finding the central location based on center of gravity method,
we have Dx = (dxA*WA + dxB*WB + dxC*WC + dxD*WD + dxE*WE + dxF*WF )/(WA + WB + WC + WD + WE + WF)
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
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 140000Related Questions
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