Question: Answer the following questions. (a) Consider a network with n nodes. Then, any shortest path between two nodes consist of at most n-2 arcs. True

Answer the following questions.

(a) Consider a network with n nodes. Then, any shortest path between two nodes consist of at most n-2 arcs. True or false? Explain.

(b) Suppose that each arc-length on a network is multiplied by the same positive constant. How would that affect the solution to the shortest path problem?

(c) Consider a network flow problem with several sources and several sinks in which the goal is to maximize the total flow into the sinks. Show how such a problem can be converted into a maximum-flow problem having only a single source and a single sink.

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