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.

(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.