Problem 2: Given the network shown below, where the labels next to the nodes e the supplies/demand. We wish to minimize the cost of this transshipment problem. Consider the darker arcs to be the spanning tree for this network. The flows for this spanning tree are given as the underlined amounts next to each arc. The numbers (Sx, y) are the costs and the capacities on each arc. (a). (25 points) Given this spanning tree, use the network simplex algorithm to determine the dual prices for this spanning tree and the associated reduced costs of all non-basic arcs (b).(25 points) Is the spanning tree optimal? If not, indicated the entering arc, the leaving are and how much flow would be increased decreased on this are and perform one pivot. If it is optimal, prove that it is by stating the optimality conditions, ie, show that there are no violating non- basic ares. ($2,6) 3, 6) 20 7,15) 1 14 ($6,25) 14 15d1s4, 5) 10 Problem 2: Given the network shown below, where the labels next to the nodes e the supplies/demand. We wish to minimize the cost of this transshipment problem. Consider the darker arcs to be the spanning tree for this network. The flows for this spanning tree are given as the underlined amounts next to each arc. The numbers (Sx, y) are the costs and the capacities on each arc. (a). (25 points) Given this spanning tree, use the network simplex algorithm to determine the dual prices for this spanning tree and the associated reduced costs of all non-basic arcs (b).(25 points) Is the spanning tree optimal? If not, indicated the entering arc, the leaving are and how much flow would be increased decreased on this are and perform one pivot. If it is optimal, prove that it is by stating the optimality conditions, ie, show that there are no violating non- basic ares. ($2,6) 3, 6) 20 7,15) 1 14 ($6,25) 14 15d1s4, 5) 10