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Transporting Grain The Sadeghian Company is in the business of buying and selling grain. An important aspect of the company's business is arranging for the purchased grain to be shipped to customers. If the company can keep freight costs low, its profitability will be improved. Currently, the company has purchased three rail cars of grain at Peoria, seven rail cars at Iowa City, and six rail cars at Lawrence. Fourteen carloads of grain have been sold. The locations and the amount sold at each location are as follows. All shipments must be routed through either Louisville or Dayton. Shown below are the shipping costs per rail car from the origins to Louisville and Dayton and the costs per rail car to ship from Louisville and Dayton to the destinations. (a) Determine a shipping schedule that will minimize the freight costs necessary to satisfy demand. (b) Show the network diagram corresponding to the solution in (a). That is, label each of the arcs in the solution and verify that the flows are consistent with the given information