3 [Total 20 pts] Figure 1 below depicts a transshipment problem, where d; and s, respectively,...

  

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3 [Total 20 pts] Figure 1 below depicts a transshipment problem, where d; and sį, respectively, represent the original demand and supply capacity (in the number of units) of node i. That is, nodes 1, 2, and 4 can produce up to 150, 200, and 120 units, respectively and need to meet the demand of 100, 150, and 130 at nodes 3, 5, and 6, respectively. Note that nodes 2, 3, and 4 are also transshipment nodes. An arrow (arc/edge) in the figure indicates the flow direction of transportation between the two nodes that it joins. For example, it is not possible to send goods from node 3 to node 1, while the reverse is possible. In addition, indicated along each edge (arrow) from i to j is the unit shipping cost from i to j. 3.a [10 pts] Formulate the problem as a transportation problem that minimizes the total shipping cost. 3.b [10 pts] Solve the problem in Problem 3.a (or the original problem.) $ = 150 10 5 20 20 =200 d₂= 100 3 6 10 12/ 54= 120 11 d,= 150 =130 Figure 1: Transshipment problem for Problem 3 Bonus [10 pts] Use the transportation problem in Problem 3.a to illustrate how a transporta- tion problem can be formulated into an assignment problem. 3 [Total 20 pts] Figure 1 below depicts a transshipment problem, where d; and sį, respectively, represent the original demand and supply capacity (in the number of units) of node i. That is, nodes 1, 2, and 4 can produce up to 150, 200, and 120 units, respectively and need to meet the demand of 100, 150, and 130 at nodes 3, 5, and 6, respectively. Note that nodes 2, 3, and 4 are also transshipment nodes. An arrow (arc/edge) in the figure indicates the flow direction of transportation between the two nodes that it joins. For example, it is not possible to send goods from node 3 to node 1, while the reverse is possible. In addition, indicated along each edge (arrow) from i to j is the unit shipping cost from i to j. 3.a [10 pts] Formulate the problem as a transportation problem that minimizes the total shipping cost. 3.b [10 pts] Solve the problem in Problem 3.a (or the original problem.) $ = 150 10 5 20 20 =200 d₂= 100 3 6 10 12/ 54= 120 11 d,= 150 =130 Figure 1: Transshipment problem for Problem 3 Bonus [10 pts] Use the transportation problem in Problem 3.a to illustrate how a transporta- tion problem can be formulated into an assignment problem.