A2 B C D E F G H J K 1 Problem 2. Wheat is harvested at farms in Nebraska and Colorado before being shipped to the three grain elevators in Kansas City. Omaha, and Des Moines. The amount of wheat harvested at each farm is 320 tons. The wheat is then shipped from grain elevators to the mills in Chicago, St. Louis, and Cincinnati. Each mill demands the following number of tons of wheat: Chicago-200, St. Louis - 100, and Cincinnati - 300. The unit shipping cost (i.e., cost per ton) between points are given in the table below. The maximum capacities of the three grain elevators are: Kansas City - 160, Omaha - 185, Des Moines - 285. Create a model to determine the best shipment plan, which meets all requirements and minimizes the total shipment cost. 2 3 Unit shipping costs (per ton) 4 5 6 7 8 9 10 11 From Nebraska Colorado Kansas City Omaha Des Moines Chicago 12 13 St. Louis Cincinnati 14 15 Network formulation (flows in tons) 16 Origin Destination 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 Total Cost 35 36 37 To Nebraska Colorado Kansas City Omaha. $19 $14 Des Moines $15 Chicago St Louis Cincinnati $18 $16 $19 $7 $11 $9 $13 13 $13 $12 $7 $7 $15 Flow balance constraints Cost Flow Index 1 Net flow out/in 2 3 4 5 6 FS1 FS2 FS3 FS4 FS5 7 8 Capacity constraint for Kansas City, Omaha, and Des Moines 3 4 5