##### Reference no: EM13332366

A cotton grower in south Georgia produces cotton on farms in Statesboro and Brooklet, ships it to cotton gins in Claxton and Millen, where it is processed, and then sends it to distribution centers in Savannah, Perry, and Valdosta, where it is sold to customers for $60 per ton. Any surplus cotton is sold to a government warehouse in Hinesville for $25 per ton. The cost of growing and harvesting a ton of cotton at the farms in Statesboro and Brooklet is $20 and $22, respectively. There are

presently 700 and 500 tons of cotton available in Statesboro and Brooklet, respectively. The cost of transporting the cotton from the farms to the gins and the government warehouse is shown in the following 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 cotton at a cost of $10 per ton. The gin in Millen can process 600 tons at a cost of $11 per ton. Each gin must use at least one half of its available capacity. The cost of shipping a ton of cotton from each gin to each distribution center is summarized in the following table:

Savannah Perry Valdosta

Claxton $10 $16 $15

Millen $12 $18 $17

Assume that the demand for cotton in Savannah, Perry, and Valdosta is 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?