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}
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}
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\section{Structure}{
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\section{Structure}{
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  Objects of class \code{"simplex"} are implemented as a list with the
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  Objects of class \code{"simplex"} are implemented as a list with the
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  following components.
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  following components.
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- 
 
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  \describe{
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  \item{soln}{
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    \item{soln}{
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    The values of \code{x} which optimize the objective function under
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      The values of \code{x} which optimize the objective function under
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    the specified constraints provided those constraints are jointly feasible.
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      the specified constraints provided those constraints are jointly feasible.
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  }
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    }
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  \item{solved}{
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    \item{solved}{
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    This indicates whether the problem was solved.  A value of \code{-1}
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      This indicates whether the problem was solved.  A value of \code{-1}
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    indicates that no feasible solution could be found.  A value of
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      indicates that no feasible solution could be found.  A value of
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    \code{0} that the maximum number of iterations was reached without
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      \code{0} that the maximum number of iterations was reached without
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    termination of the second stage.  This may indicate an unbounded
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      termination of the second stage.  This may indicate an unbounded
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    function or simply that more iterations are needed. A value of
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      function or simply that more iterations are needed. A value of
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    \code{1} indicates that an optimal solution has been found.
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      \code{1} indicates that an optimal solution has been found.
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  }
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    }
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  \item{value}{
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    \item{value}{
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    The value of the objective function at \code{soln}.
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      The value of the objective function at \code{soln}.
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  }
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    }
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  \item{val.aux}{
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    \item{val.aux}{
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    This is \code{NULL} if a feasible solution is found. Otherwise it is
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      This is \code{NULL} if a feasible solution is found. Otherwise it is
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    a positive value giving the value of the auxiliary objective
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      a positive value giving the value of the auxiliary objective
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    function when it was minimized.
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      function when it was minimized.
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  }
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    }
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  \item{obj}{
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    \item{obj}{
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    The original coefficients of the objective function.
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      The original coefficients of the objective function.
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  }
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    }
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  \item{a}{
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    \item{a}{
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    The objective function coefficients re-expressed such that the basic
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      The objective function coefficients re-expressed such that the basic
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    variables have coefficient zero.
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      variables have coefficient zero.
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  }
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    }
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  \item{a.aux}{
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    \item{a.aux}{
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    This is \code{NULL} if a feasible solution is found. Otherwise it is the
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      This is \code{NULL} if a feasible solution is found. Otherwise it is the
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    re-expressed auxiliary objective function at the termination of the first
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      re-expressed auxiliary objective function at the termination of the first
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    phase of the simplex method.
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      phase of the simplex method.
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  }
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    }
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  \item{A}{
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    \item{A}{
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    The final constraint matrix which is expressed in terms of the
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      The final constraint matrix which is expressed in terms of the
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    non-basic variables.  If a feasible solution is found then this will
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      non-basic variables.  If a feasible solution is found then this will
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    have dimensions \code{m1+m2+m3} by \code{n+m1+m2}, where the final
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      have dimensions \code{m1+m2+m3} by \code{n+m1+m2}, where the final
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    \code{m1+m2} columns correspond to slack and surplus variables.  If
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      \code{m1+m2} columns correspond to slack and surplus variables.  If
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    no feasible solution is found there will be an additional
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      no feasible solution is found there will be an additional
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    \code{m1+m2+m3} columns for the artificial variables introduced to
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      \code{m1+m2+m3} columns for the artificial variables introduced to
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    solve the first phase of the problem.
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      solve the first phase of the problem.
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  }
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    }
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  \item{basic}{
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    \item{basic}{
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    The indices of the basic (non-zero) variables in the solution.
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      The indices of the basic (non-zero) variables in the solution.
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    Indices between \code{n+1} and \code{n+m1} correspond to slack
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      Indices between \code{n+1} and \code{n+m1} correspond to slack
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    variables, those between \code{n+m1+1} and \code{n+m2} correspond to
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      variables, those between \code{n+m1+1} and \code{n+m2} correspond to
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    surplus variables and those greater than \code{n+m2} are artificial
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      surplus variables and those greater than \code{n+m2} are artificial
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    variables.  Indices greater than \code{n+m2} should occur only if
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      variables.  Indices greater than \code{n+m2} should occur only if
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    \code{solved} is \code{-1} as the artificial variables are discarded in
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      \code{solved} is \code{-1} as the artificial variables are discarded in
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    the second stage of the simplex method.
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      the second stage of the simplex method.
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  }
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    }
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  \item{slack}{
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    \item{slack}{
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    The final values of the \code{m1} slack variables which arise when
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      The final values of the \code{m1} slack variables which arise when
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    the "<=" constraints are re-expressed as the equalities
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      the "<=" constraints are re-expressed as the equalities
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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
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    original constraints.  A feasible solution exists only if all of the
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      original constraints.  A feasible solution exists only if all of the
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    artificial variables can be made 0 simultaneously.
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      artificial variables can be made 0 simultaneously.
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    }
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  }
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  }
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}
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}
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\seealso{
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\seealso{
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  \code{\link{print.simplex}}, \code{\link{simplex}}
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  \code{\link{print.simplex}}, \code{\link{simplex}}
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}
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}