please answe only 10-31 ( the first pic ) part B and C

10-31 The Quick Chip gravel company has received a contract to supply two new construction projects in the towns of Brock and Wurst. A total of 60 truckloads are needed at Brock in the next month and 90 at Wurst. Quick Chip has idle gravel pits in the towns of Nova, Scova, and Tova, each with a monthly production capacity of 50 truckloads. Travel distances from each pit to each project site are shown in the following table. To Brock Pit To Wurst Nova 23 77 Scova 8 94 Tova 53 41 The company wants to fulfill its contract at least total truck travel distance Formulate a linear program to choose an optimal shipping plan. (b) Use class optimization software to compute an optimal solution to your LP. >> Show that your LP can be represented as a minimum cost transportation problem by sketching the corresponding bipartite digraph and labeling as in Exercise 10-10. EXERCISES 10-1 The figure that follows depicts a minimum cost network flow problem. Numbers on the nodes show net demand, while those on arcs show unit cost and capacity. -50 (1 (5.00) 2 20 (10.40) 0 (8.20) 4 (-6,4) (6,00) (0, 10) (OCD) (2,00) (3,00) -703 5) 100 (a) Identify the node set V and the arc set A of the network. (b) Classify all nodes as source, sink, or transshipment. (c) Verify that total supply equals total demand. (d) Formulate the corresponding minimum cost network flow problem as a linear program. (e) Show the node-arc incidence matrix for the network