21 May WHAT IS THE OPTIMAL SOLUTION?
A cotton grower in south Georgia produces cotton on farms inStatesboro and Brooklet, ships it to cotton gins in Claxton andMillen, where it is processed, and then sends it to distributioncenters in Savannah, Perry, and Valdosta, where it is sold tocustomers for $60 per ton. Any surplus cotton is sold to agovernment warehouse in Hinesville for $25 per ton. The cost ofgrowing and harvesting a ton of cotton at the farms in Statesboroand Brooklet is $20 and $22, respectively. There are presently 700 and 500 tons of cotton available in Statesboro andBrooklet, respectively. The cost of transporting the cotton fromthe farms to the gins and the government warehouse is shown in thefollowing table:
Claxton Millen Hinesville
Statesboro $4.00 $3.00 $4.50
Brooklet $3.50 $3.00 $3.50
The gin in Claxton has the capacity to process 700 tons of cottonat a cost of $10 per ton. The gin in Millen can process 600 tons ata cost of $11 per ton. Each gin must use at least one half of itsavailable capacity. The cost of shipping a ton of cotton from eachgin to each distribution center is summarized in the followingtable:
Savannah Perry Valdosta
Claxton $10 $16 $15
Millen $12 $18 $17
Assume that the demand for cotton in Savannah, Perry, and Valdostais 400, 300, and 450 tons, respectively.
a. Draw a network flow model to represent the problem.
b. Implement your model in Excel and solve it.
c. What is the optimal solution?
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