# Real-Life Experience with Maximizing or Minimizing and Application to Linear Programming; Geometric Discussion of the Simplex Method; Computer Programs for Linear Programming

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1) Discuss from your own experience a case where you had to maximize or minimize something and also how you think linear programming techniques might have helped you arrive at your final decision.

2) Read the short, well-written article on the Simplex Method which appears here:

http://www.sce.carleton.ca/faculty/chinneck/po/Chapter4.pdf

Discuss what is going on geometrically inside the Simplex Method.

3) Do a search using an Internet search engine and discuss some of the many computer algorithms and programs that exist to solve linear programming problems.

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(See attached file for full problem description)

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#### Solution Preview

1) Discuss from your own experience a case where you had to maximize or minimize something and also how you think linear programming techniques might have helped you arrive at your final decision.

If I want to visit several cities (say 8 cities) in one week, while want to minimize the total distance that I travel ( so that I can minimize my trip cost), then I have to find the best path ( such as 1 3 5 2 4 7 8). This is a linear programming problem, and by formulating it properly, it can help me find the best solution.

Another example, minimizing shipping cost:

There are m product sources S1,S2, ... Sm, which are to be ...

#### Solution Summary

Real-Life Experience with Maximizing or Minimizing and Application to Linear Programming; Geometric Discussion of the Simplex Method; Computer Programs for Linear Programming are investigated. The solution is detailed and well presented.