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      \code{A1\%*\%x + slack = b1}.
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      \code{A1\%*\%x + slack = b1}.
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    }
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    }
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    \item{surplus}{
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    \item{surplus}{
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      The final values of the \code{m2} surplus variables which arise when
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      The final values of the \code{m2} surplus variables which arise when
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      the "<=" constraints are re-expressed as the equalities \code{A2\%*\%x -
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      the "<=" constraints are re-expressed as the equalities \code{A2\%*\%x -
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	surplus = b2}.
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        surplus = b2}.
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    }
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    }
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    \item{artificial}{
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    \item{artificial}{
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      This is NULL if a feasible solution can be found.  If no solution
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      This is NULL if a feasible solution can be found.  If no solution
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      can be found then this contains the values of the \code{m1+m2+m3}
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      can be found then this contains the values of the \code{m1+m2+m3}
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      artificial variables which minimize their sum subject to the
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      artificial variables which minimize their sum subject to the