Walsh€™s Fruit Company contracts with growers in Ohio, Pennsylvania, and New York to purchase grapes. The grapes are processed into juice at the farms and stored in refrigerated vats. Then the juice is shipped to two plants, where it is processed into bottled grape juice and frozen concentrate. The juice and concentrate are then transported to three food warehouses/distribution centers. The transportation costs per ton from the farms to the plants and from the plants to the distributors, and the supply at the farms and demand at the distribution centers are summarized in the following tables:

a. Determine the optimal shipments from farms to plants to distribution centers to minimize total transportation costs.
b. What would be the effect on the solution if the capacity at each plant were 140,000tons?

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Plant 4. Indiana $16 18 5. Georgia 21 16 25 Supply (1,000 tons) 72 105 83 Farm 1. Ohio 2. Pennsylvania 3. New York Distribution Center 6. Virginia . Kentucky 8. Louisiana Plant 4. Indiana 5. Georgia Demand (1,000 tons) $29 24 $23 20 90 17 80 120