Network Analysis The figure shows the flow of traffic (in vehic... | Filo

Draw a signal flow graph for the block diagram and use Mason's ... | Filo

Consider the following network flow problem:The numbers above t... | Filo

SOLVED:Exercise 7.17 Consider a network flow problem and assume that there exists at least one feasible solution. We wish to show that the optimal cost is ~O0 if and only if there exists a negative cost directed cycle such that every arc on the cycle has infinite capacity: (a) Provide proof based on the flow decomposition theorem. (b) For uncapacitated problems, provide proof based on the network simplex method_

In a standard s-t Maximum-Flow Problem, we assume edges have capaci ties, and there is no limit on how much flow is allowed to pass through a node. In this problem, we consider the variant of the Maximum-Flow and Minimum-Cut problems with node capacities. Let G=(V, E) be a directed graph, with source s ∈V, sink t ∈V, and nonnegative node capacities {cv ≥0} for each v ∈V. Given a flow f in this graph, the flow though a node v is defined as f^in (v). We say that a flow is feasible if it satisfies