Wheat is harvested at farms in Nebraska and Colorado before being shipped to the three-grain elevators in Kansas City, Omaha, and Des Moines, which are now transshipment points. The amount of wheat harvested at each farm is 300 tons. The wheat is then shipped to the mills in Chicago, and Grand Forks. The shipping costs from the grain elevators to the mills and demand of each mill, and the shipping cost from the farms to the grain elevators are as follows:
Grain Elevator
Farm Kansas City (3) Omaha (4) Des Moines (5)
Nebraska (1) $16 $10 $12
Colorado (2) $15 $14 $17
Mills
Grain Elevator Chicago (6) Grand Forks (7)
Kansas City (3) $ 6 $ 8
Omaha (4) $10 $11
Des Moines (5) $ 4 $12
Demand 400 100
a) Define decision variables
b) Define objective function