Wheat is harvested at two farms in Nebraska and Colorado before being shipped to three grain elevators in Kansas City, Omaha, and Des Moines. The amount of wheat harvested at each of the two farms is 300 tons. After reaching the grain elevators, the wheat is then shipped on to processing mills in Chicago, St. Louis, and Cincinnati. The demand at the three mills is: Chicago (200 tons), St. Louis (100 tons), and Cincinnati (300 tons). The various shipping costs per ton shipped from the farms to the grain elevators is shown in the following table:
Farm Grain Elevator
Kansas City Omaha Des Moines
Nebraska $16 $10 $12
Colorado $15 $14 $17
The shipping costs per ton shipped from the three grain elevators to each of the three processing mills is shown in the following table:
Grain Elevator Processing Mills
Chicago St. Louis Cincinnati
Kansas City $6 $8 $10
Omaha $7 $11 $11
Des Moines $4 $5 $12
What is the optimal shipping schedule from each of the farms to each of the grain elevators and what is the optimal shipping schedule from each of the grain elevators to each of the processing mills? What is the total shipping cost of this schedule?
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