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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: Plant 4. Indiana 5. Georgia Supply (1,000 tons) $16 21 72 16 105 25 83 Farm 1. Ohio 2. Pennsylvania 18 3. New York 22 Distribution Center Plant 6. Virginia 7. Kentucky 8. Louisiana 4. Indiana $23 $15 $29 5. Georgia 20 17 24 Demand (1,000 tons) 90 80 120 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 140,000 tons?

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: Plant 4. Indiana 5. Georgia Supply (1,000 tons) $16 21 72 16 105 25 83 Farm 1. Ohio 2. Pennsylvania 18 3. New York 22 Distribution Center Plant 6. Virginia 7. Kentucky 8. Louisiana 4. Indiana $23 $15 $29 5. Georgia 20 17 24 Demand (1,000 tons) 90 80 120 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 140,000 tons?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Question: 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: Plant Farm 1. Ohio 2. Pennsylvania 18 3. New York 22 4. Indiana 5. Georgia Supply (1,000 tons) $16 21 72 16 105 25 Plant 83 Distribution Center 6. Virginia 7. Kentucky 8. Louisiana 4. Indiana $23 $15 $29 5. Georgia 20 17 24 Demand (1,000 tons) 90 80 120 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 140,000 tons?
Transcribed Image Text:Question: 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: Plant Farm 1. Ohio 2. Pennsylvania 18 3. New York 22 4. Indiana 5. Georgia Supply (1,000 tons) $16 21 72 16 105 25 Plant 83 Distribution Center 6. Virginia 7. Kentucky 8. Louisiana 4. Indiana $23 $15 $29 5. Georgia 20 17 24 Demand (1,000 tons) 90 80 120 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 140,000 tons?
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