I have this problem. I am trying to do it in excel, but when I add my constrains and all my info to my solver, it doesn't change anything. I don't know what I am doing wrong.

Farm 1. Ohio 2. Pennsylvania 3. New York Plant 4. Indiana 5. Georgia Supply (1,000 tons) 16 21 72 18 16 105 22 25 83 Farm 1. Ohio 2. Pennsylvania 3. New York Shipped Plant 4. Indiana 5. Georgia Supply (1,000 tons) 0 0 72 0 0 105 0 0 0 83 0 0 0 Shipped 0 0 0 0 Plant 4. Indiana 5. Georgia Demans (1,000) Distribution Center 6. Virginia 7. Kentucky 8. Lousiana 23 15 29 20 17 24 90 80 -D10 Shipped 0 0 Distribution Center Plant 6. Virginia 7. Kentucky 8. Lousiana 4. Indiana 0 0 0 5. Georgia 0 0 0 Demans (1,000) 0 0 0 0 Shipped 0 0 0 Transshipments flows (Technical Constraints). 4. Indiana 0 5. Georgia 0 Set Objective: 0 Cost Solver Parameters $G$14 Value Of: 0 Linear Programming Model: Min Z = 16 x14 + 21 x15 +18 x24 + 16 x25 + 22 x34 + 25x35 + 23 x46 + 15 x47 + 29x48 +20 x56 +17 x57 +24 x58 To: Max O Min By Changing Variable Cells: $G$3:5H$5 Subject to: Total Supply = 260,000 tons Total Demand = 290,000 tons Add Subject to the Constraints: $G$10:$1$11 >=0 $G$12:$1$12 - $B$11:$D$11 $G$3:$H$5 > 0 $J$3:$J$5 = 0 Make Unconstrained variables Non-Negative Select a Solving Method Simplex LP Options A B B D E F G H Shipped 0 0 0 Shipped 0 0 1 Plant Plant 2 Farm 4. Indiana 5. Georgia Supply (1,000 tons) ) Farm 4. Indiana 5. Georgia Supply (1,000 tons) 3 1. Ohio 16 21 72 1. Ohio 0 0 72 4 2. Pennsylvania 18 16 105 2. Pennsylvania 0 0 105 5 3. New York 22 25 83 3. New York 0 0 83 6 Shipped 0 0 0 7 Distribution Center 8 Plant 6. Virginia 7. Kentucky 8. Lousiana Distribution Center 9 4. Indiana 23 15 29 Plant 6. Virginia 7. Kentucky 8. Lousiana 10 5. Georgia 20 17 24 4. Indiana 0 0 0 11 Demans (1,000) 90 80 120 5. Georgia 0 0 0 12 Demans (1,000) 0 0 0 13 Shipped 0 0 0 14 Cost 0 15 Transshipments flows (Technical Constraints). 16 4. Indiana 0 17 5. Georgia 0 0 18 19 20 Linear Programming Model: 21 Min Z = 16 x14 + 21 x15 +18 x24 + 16 x25 + 22 x34 + 25x35 + 23 x46 + 15 x47 + 29x48 +20 x56 +17 x57 +24x58 22 23 Subject to: 24 Total Supply = 260,000 tons 25 Total Demand = 290,000 tons 26 27 Unbalaced model 28 x14 + x15 = 0 32. 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: Farm Plant Supply (1,000 tons) 4. Indiana 5. Georgia 1. Ohio $16 21 72 2. Pennsylvania 18 16 105 3. New York 22 25 83 Distribution Center Plant 6. Virginia 7. Kentucky 8. Louisiana 4. Indiana $23 $15 $ 29 5. Georgia 20 17 24 at the farms and demand at the distribution centers are summarized in the following tables: Farm Plant Supply (1,000 tons) 4. Indiana 5. Georgia 1. Ohio $16 21 72 2. Pennsylvania 18 16 105 3. New York 22 25 83 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