The Midlands Field Produce Company contracts with potato farmers in Colorado, Minnesota, North Dakota, and Wisconsin for monthly potato shipments. Midlands picks up the potatoes at the farms and ships mostly by truck (and sometimes by rail) to its sorting and distribution centers in Ohio, Missouri, and Iowa. At these centers the potatoes are cleaned, rejects are discarded, and the potatoes are sorted according to size and quality. They are then shipped to combination plants and distribution centers in Virginia, Pennsylvania, Georgia, and Texas, where the company produces a variety of potato products and distributes bags of potatoes to stores. Exceptions are the Ohio distribution center, which will accept potatoes only from farms in Minnesota, North Dakota, and Wisconsin, and the Texas plant, which won€™t accept shipments from Ohio 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):

Formulate and solve a linear programming model to determine the optimal monthly shipments from the farms to the distribution centers and from the distribution centers to the plants to minimize total shipping and processingcosts.

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Distribution Center (S/bushel) 5. Ohio 6. Missouri 7. lowa $1.26 1.17 1.36 1.42 Supply (bushels) 1.600 1.100 1400 1.900 Farm 1. Colorado 2. Minnesota 3. North Dakota 4. Wisconsin $1.09 1.32 1.22 1.25 2,200 0.89 0.78 Processing Capacity (bushels) 1,800 1,600 Plant (S/bushel) Distribution Center 8. Virginia 9. Pennsylvania 10. Georgia 5. Ohio 6. Missouri 7. lowa Demand (bushels) Texas S4.56 3.43 5.39 1.200 $3.98 5.74 6.35 900 54.94 4.65 5.70 1,100 5.01 4.87 1,500