\Header{simplex.object}{Linear Programming Solution Objects}
\keyword{optimize}{simplex.object}
\keyword{methods}{simplex.object}
\begin{Description}\relax
Class of objects that result from solving a linear programming
problem using \code{simplex}.
\end{Description}
\begin{Section}{Generation}
This class of objects is returned from calls to the function \code{simplex}.
\end{Section}
\begin{Section}{Methods}
The class \code{"saddle.distn"} has a method for the function \code{print}.
\end{Section}
\begin{Section}{Structure}
Objects of class \code{"simplex"} are implemented as a list with the
following components.

\item[soln] The values of \code{x} which optimize the objective function under
the specified constraints provided those constraints are jointly feasible.

\item[solved] This indicates whether the problem was solved.  A value of \code{-1}
indicates that no feasible solution could be found.  A value of
\code{0} that the maximum number of iterations was reached without
termination of the second stage.  This may indicate an unbounded
function or simply that more iterations are needed. A value of
\code{1} indicates that an optimal solution has been found.

\item[value] The value of the objective function at \code{soln}.

\item[val.aux] This is \code{NULL} if a feasible solution is found. Otherwise it is
a positive value giving the value of the auxiliary objective
function when it was minimized.

\item[obj] The original coefficients of the objective function.

\item[a] The objective function coefficients re-expressed such that the basic
variables have coefficient zero.

\item[a.aux] This is \code{NULL} if a feasible solution is found. Otherwise it is the
re-expressed auxiliary objective function at the termination of the first
phase of the simplex method.

\item[A] The final constraint matrix which is expressed in terms of the
non-basic variables.  If a feasible solution is found then this will
have dimensions \code{m1+m2+m3} by \code{n+m1+m2}, where the final
\code{m1+m2} columns correspond to slack and surplus variables.  If
no feasible solution is found there will be an additional
\code{m1+m2+m3} columns for the artificial variables introduced to
solve the first phase of the problem.

\item[basic] The indices of the basic (non-zero) variables in the solution.
Indices between \code{n+1} and \code{n+m1} correspond to slack
variables, those between \code{n+m1+1} and \code{n+m2} correspond to
surplus variables and those greater than \code{n+m2} are artificial
variables.  Indices greater than \code{n+m2} should occur only if
\code{solved} is \code{-1} as the artificial variables are discarded in
the second stage of the simplex method.

\item[slack] The final values of the \code{m1} slack variables which arise when
the "<=" constraints are re-expressed as the equalities
\code{A1\%*\%x + slack = b1}.

\item[surplus] The final values of the \code{m2} surplus variables which arise when
the "<=" constraints are re-expressed as the equalities \code{A2\%*\%x -
      surplus = b2}.

\item[artificial] This is NULL if a feasible solution can be found.  If no solution
can be found then this contains the values of the \code{m1+m2+m3}
artificial variables which minimize their sum subject to the
original constraints.  A feasible solution exists only if all of the
artificial variables can be made 0 simultaneously.
\end{Section}
\begin{SeeAlso}\relax
\code{\Link{print.simplex}}, \code{\Link{simplex}}
\end{SeeAlso}

