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MathGroup Archive 2006

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OT: simplex method

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66352] OT: simplex method
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Wed, 10 May 2006 06:34:25 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello MathGroup,
This is more of a numerical methods question than a Mathematica
question. Please forgive the off topic post. I just feel that you are
mathematically knowledgeable people and might be inclined to provide
instructive input.

First, this is a homework problem, so if you don't want to help me
with homework - uh... forget what I just told you and continue
reading.

Here is a Linear Programming problem I am trying to solve:

eq=And[F==2*X[1]+4*X[2],2*X[1]+X[2]>=2,X[1]>=0,X[2]>=0]

Asking Mathematica for the answer (minimum of F) is trivial.

Minimize[{Last@First@eq,Rest@eq},List@@eq[[{-2,-1},1]]]

If I want to solve it via the simplex method, here is the tableau

{{2,1,-1,2},{2,4,0,F}}

The only problem is, I can't see where I would be able to create a
basis of two variables if I only have one constraint. I have solved
all the other linear programming problems thrown at me so far, but
this one leaves me scratching my head. I have tried augmenting the
tableau with extra variables and also tried expressing the X[1]>0,
X[2]>0 constraints in the tableau, but both avenues didn't yield an
answer.

Could someone please explain what is happening in this problem and how
one should apply the simplex method in this case?

Thank you,
--
http://chris.chiasson.name/


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