# Using the Simplex algorithm to solve systems of linear inequalities?

I am trying to understand how I could use the first phase of the Simplex method (i.e. constructing a tableaux corresponding to an initial feasible solution) in order to solve systems of linear inequalities.

For example, consider the trivial:

1. a <= b
2. b <= c

I can introduce slack variables to get rid of the inequalities:

1. a - b + s1 = 0
2. b - c + s2 = 0

However, in order to use Simplex, don't I need to introduce an objective function as well in order to find the initial feasible solution? If this is the case, could this objective function simply be a function of the slack variables?

1. Minimize P = s1 + s2, subject to:
2. a - b + s1 = 0
3. b - c + s2 = 0

Is this the correct way to go about it, or is there something I am missing?

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Why would you want to do that? There are easier ways to solve systems of linear equations... – fgp May 12 '13 at 13:03
You are right, the subject is supposed to read "systems of linear inequalities", not equations. Fixing. – csvan May 12 '13 at 13:04