The MidAm Produce Company contracts with potato farmers in Idaho, Nebraska; South Dakota; and Michigan for monthly potato shipments. MidAm picks up the potatoes at the farms and ships mostly by truck (and sometimes by rail) to its sorting and distribution centers in Indiana, Kansas, and Arkansas. At these centers the potatoes are cleaned, rejects are discarded, and they are sorted according to size and quality. They are then shipped to combination plants and distribution centers in Maryland, Ohio, South Carolina, and Alabama where the company produces a variety of potato products and distributes bags of potatoes to stores. An exception is the Indiana distribution center which will only accept potatoes from farms in Nebraska, South Dakota, and Michigan, and the Alabama plant which won€™t accept shipments from Indiana because of disagreements over delivery schedules and quality issues. Following are summaries of the shipping costs from the farms to the distribution centers and the processing and shipping costs from the distribution centers to the plants, as well as the available monthly supply at each farm, the processing capacity at the distribution centers, and the final demand at the plants (in bushels).

Determine the optimal monthly shipments from the farms to the distribution centers and from the distribution centers to the plants that will minimize total shipping and processingcosts.

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Dis tribution Centers ($/bushel 5. Indiana 6.Kans as 7.Arkans as Supply (bushels Farm 1.daho Nebraska9132 1.1 3. South Dakota 0.78 1.22 1.36 Michigan125 1.2 Processing 00 2200 ,600 Capacity (bushols 1.09 1,600 1,100 1,400 1.900 Plants (S/bushol) Distribution Center 5. Indiana 6. Kansas .Arkansas Demand lbushels] 1,200 00 100 1500 10. South 8.Maryland 9.Oblo Carolina 11.Alabama 3.98 494 456 43 574 465 5.01 5.39 635 5.70 4.87