Special Test To Whom It May Concern

Instruction : Answer All Questions

Please send your answers to beejark@yahoo.com

1) The Standard Maximum Flow Problem

Let G = (V,E) be a directed graph with vertex set V and edge set E. Size of set V is n and size of set E is m. G has two distinguished vertices, a source s and a sink t. The network was shown as below.

By using The Maximum Flow Algorithm solve this problem and

get the value in the sink (T) from source (S).

2) Minimum spanning trees

Basically a minimum spanning tree is a subset of the edges of the graph, so that there’s a path form any node to any other node and that the sum of the weights of the edges is minimum.

Here’s the minimum spanning tree of the example:

Look at the above image closely. It contains all of the initial nodes and some of the initial edges. Actually it contains exactly n – 1 edges, where n is the number of nodes. It’s called a tree because there are no cycles.

You can think of the graph as a map, with the nodes being cities, the edges passable terrain, and the weights the distance between the cities.

It’s worth mentioning that a graph can have several minimum spanning trees. Think of the above example, but replace all the weight with 1. The resulting graph will have 6 minimum spanning trees.

Given a graph, find one of its minimum spanning trees.

3) Simplex Method

Maximize Z = 2x1 - 3x2 + 4x3 subject to
4x1 + 2x2 + x3 10 x1 + x2 - x3 5 x1 , x2 , x3 0. 4) Discuss in detail how Operational Research mat help you to solve the real life problems including your decision making. (your answer should be at least 200 words)