Directed network

Figure 1 shows a capacitated, directed network. The number on each arc represents the capacity of that arc. The numbers in circles represent an initial flow.

(a) State the value of the initial flow.

(b) Complete the initialisation of the labelling procedure on Diagram 1 in the answer book by entering values along SC, AB, CE, DE and DT.

(c) Hence use the labelling procedure to find a maximum flow through the network. You must list each flow-augmenting route you use, together with its flow.

(d) Draw a maximal flow pattern on Diagram 2 in the answer book.

(e) Prove that your flow is maximal.