A farmers\' cooperative association plans to build a new sugar mill in Southwest
ID: 376667 • 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. 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.
Explanation / Answer
Volume weighted center of gravity :
East of lake Charles = 83,500 / 1150 = 72.60
North of lake Charles = 58,000 / 1150 = 50.47
Simple center of gravity (all cities weighted equally)
East of lake Charles = 90 + 140 + 20 + 50 + 100 / 5 = 400/5 = 80
North of Lake Charles = 10 + 60 + 70 + 20 + 80 / 5 = 240/5 = 48
The two calculations differ because, with heavy tonnage, the coordinates differ. The heaviest tonnage is from Cancienne. But in simple center of gravity, coordinates are as per the distances and not the volume.
Village East (x) North (y) Vol ('000) X-multiplied Y-multiplied A 90 10 250 22,500 2500 B 140 60 300 42,000 18000 C 20 70 450 9000 31,500 D 50 20 100 5000 2000 E 100 80 50 5000 4000 Total 400 240 1,150 83,500 58,000Related Questions
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