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Given a transportation problem with the following costs, supply and demand, find the optimal solution. To (cost) From 2 3 Supply $ $ 100 180 200 Demand 135 150 170A 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 4. Indiana 5. Georgia Supply (1,000 tons) 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 Determine the optimal shipments from farms to plants to distribution centers to minimize total transportation costs.The football coaching staff at Tech focuses its recruiting on several key states, including Georgia, Florida, Virginia, Pennsylvania, New York, and New Jersey. The staff includes seven assistant coaches, two of whom are responsible for Florida, a high school talent-rich state, whereas one coach is assigned to each of the other five states. The staff has been together for a long time, and at one time or another all the coaches have recruited in all the states. The head coach has accumulated some data on the past success rate (i.e., percentage of targeted recruits signed) for each coach in each state, as shown in the following table: State Coach GA FL VA PA NY NJ Allen 62 56 65 71 55 63 Bush 65 70 63 81 75 72 Crumb 46 53 62 55 64 50 Doyle 58 66 70 67 71 49 Evans 77 73 69 80 80 74 Fouch 68 73 72 80 78 57 Goins 72 60 74 72 62 61 Determine the optimal assignment of coaches to recruiting regions that will maximize the overall success rate and indicate the average percentage success rate for the staff with this assignment