Flows in a network question

3. This question is about flows in a network. (a) Apply the Ford-Fulkerson algorithm to compute the maximum flow from s tot in the following network. Show your working and state the maximum flow. (10 marks] 3 (b) Give a cut in the network of minimal capacity, and justify why it is minimal. (5 marks) (c) The following network contains not only capacities, but also minimal flows along each edge. For example, the edge labelled (1,2) must have a flow of value between 1 and 2. Is there a flow from s tot that satisfies all of the labels on the edges? Justify your answer. [10 marks] n (1.4) (1,2) (1,6) 12,4) 15,7) [Hint: you might find it useful to add an edge from t to s with large capacity, and then consider it as a circulation with demands and lower bounds]