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Starting out with linear programming, I'm having some questions about canonical linear programs:

  • Do all linear programs have a canonical form? So far I couldn't figure an example stating otherwise.

  • Can a linear program have different (multiple) canonical forms? I guess the answer is yes. Are all forms equally good for solving the program? Is there any relevant difference?

  • A "basic feasible solution" is a feasible solution where the non-basic variables are equalled to 0. Is there only one "basic feasible solution" for each canonical linear program?

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The answers are: 1) YES; 2) YES/more or less/not much ; 3) NO.

You an easily find all the details on any standard textbook as

"Combinatorial Optimization: Algorithms and Complexity" Book by Christos Papadimitriou and Kenneth Steiglitz

or

Linear and Nonlinear Programming: Second Edition by David G. Luenberger

but the Internet is full of material on that.

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