5.1 [10 marks] We consider a minimum cost network flow problem on the following digraph: 1 2 3 4. 5 6 7 8 9 The supply b is nonzero at three nodes: b(4) = 2, 6(7) = -1, b(9) = -1. The thick arcs form a tree, if we ignore the directions. (a) Determine a balanced tree solution for this tree. (b) If for every arc (i,j) that is drawn we assume a cost of Cij = 1, and if we take the node 5 as the root, determine the dual variables for each node. 5.1 [10 marks] We consider a minimum cost network flow problem on the following digraph: 1 2 3 4. 5 6 7 8 9 The supply b is nonzero at three nodes: b(4) = 2, 6(7) = -1, b(9) = -1. The thick arcs form a tree, if we ignore the directions. (a) Determine a balanced tree solution for this tree. (b) If for every arc (i,j) that is drawn we assume a cost of Cij = 1, and if we take the node 5 as the root, determine the dual variables for each node