# Shortest Path and Maximal Flow Problem

Please see the attached file for the fully formatted problems.

1. Shortest Path and Maximal Flow Problem (30%): You are given the following directed network.

[NETWORK]

a. (Shortest Path Problem 15%) Let the numbers on the arcs represent distances and find the shortest path from node 1 to node 9.

b. (Maximal Flow Problem 15%) Let the numbers represent flow capacity and find the maximum flow from node 1 to node 9.

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#### Solution Preview

1. Shortest Path and Maximal Flow Problem (30%): You are given the following directed network.

a. (Shortest Path Problem 15%) Let the numbers on the arcs represent distances and find the shortest path from node 1 to node 9.

This is a shortest route problem. Following are the steps to follow.

1. Find the nearest node to the origin. Put the distance in a box by the node.

Nearest node to node 1 is node 2 at a distance of 3.

2. Find the next nearest node to the origin, and put the distance in a box by the node. In some cases, several paths will have to be checked to find the nearest ...

#### Solution Summary

This posting contains solution to following problems on Shortest Path and Maximal Flow technique.