Grove Food Products Company has contracted with apple growers in Wisconsin, lowa, and Virginia to purchase apples, which the company then ships to its plants in Ohio and Alabama where it is processed into apple juice. Each bushel of apples will produce two gallons of apple juice. The juice is canned and bottled at the plants and shipped by rail and truck to warehouse/distribution centers in Pennsylvania, Tennessee, and North Carolina. The shipping costs per bushel from the farms to the plants and the shipping costs per gallon from the plants to the distribution centers are summarized in the following tables.

Formulate and solve a linear programming model to determine the optimal shipments from the farms to the plants and from the plants to the distribution centers that will minimize total shippingcosts

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Plant 4.0hio 5.Alabama Supply (bushels) Farm 1. Wisconsin 2. lowa 3. Virginia Plant Capacity 42 .39 .52 5,000 27,000 16,000 35,000 .56 34,000 Plant6.Pennsylvania 7. Tennessee 8. North Carolina 4. Ohio 5. Alabama 24 .12 .18 14,000 .21 19 16,000 Demand (gals) 10,000