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# Optimal Path: Maximum flow

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A maximum flow problem to find the maximum amount of water to flow from city 1 to city 10.

https://brainmass.com/math/graphs-and-functions/optimal-path-maximum-flow-513270

#### Solution Preview

I attached a word file with a detailed step-by-step explanation of the method and results, including 10 diagrams on how we can solve this algorithm by hand instead of a computer software. Thank-you for using BrainMass.

Preview:

This is a maximum flow problem as we need the maximum amount of water to flow from city 1 to city 10. The Ford-Fulkerson algorithm determines the maximum flow of the network. The Ford and Fulkerson algorithm states that in such problems exist two notable vertices. The first, the source, has intake 0 (in this case city 1) and the second, the sink, (in this case city 10) has outtake 0. Therefore all flow has to get from the source to the sink through possible paths in the system.

The capacity of paths in the network (i,j) is ...

#### Solution Summary

This is a 7 page long step by step explanation and demonstration, through a numerical example and the use of 12 graphs, of the maximum flow problem with the use of the Ford-Fulkerson algorithm.

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