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. Presently, 700 and 500 tons of cotton are available in Statesboro and Brooklet, respectively. The cost of transporting the cotton from the farms to the gins is shown in the following table:
|
Claxton
|
Millen
|
|
|
Statesboro
|
$4.00
|
$3.00
|
|
Brooklet
|
$3.5
|
$3.00
|
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
|
The demand for cotton in Savannah, Perry, and Valdosta is 400, 300, and 450 tons, respectively. The trucks used to ship the cotton can hold a maximum of 400 tons. The cotton grower would like to meet the demand with the minimal shipping cost.
a. Draw a network flow model to represent this problem. Make sure that you note all the numerical information about each node and each arc appropriately on the graph using network modeling convention (if you prefer, you can take a picture of your drawing and paste it to your file).
b. Implement your model in Excel and solve it.
c. What is the optimal solution? You can summarize your solution in a table or in a graph.