simplex.object {boot}  R Documentation 
Linear Programming Solution Objects
Description
Class of objects that result from solving a linear programming
problem using simplex
.
Generation
This class of objects is returned from calls to the function simplex
.
Methods
The class "saddle.distn"
has a method for the function print
.
Structure
Objects of class "simplex"
are implemented as a list with the
following components.
 soln

The values of
x
which optimize the objective function under the specified constraints provided those constraints are jointly feasible.  solved

This indicates whether the problem was solved. A value of
1
indicates that no feasible solution could be found. A value of0
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 of1
indicates that an optimal solution has been found.  value

The value of the objective function at
soln
.  val.aux

This is
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.  obj

The original coefficients of the objective function.
 a

The objective function coefficients reexpressed such that the basic variables have coefficient zero.
 a.aux

This is
NULL
if a feasible solution is found. Otherwise it is the reexpressed auxiliary objective function at the termination of the first phase of the simplex method.  A

The final constraint matrix which is expressed in terms of the nonbasic variables. If a feasible solution is found then this will have dimensions
m1+m2+m3
byn+m1+m2
, where the finalm1+m2
columns correspond to slack and surplus variables. If no feasible solution is found there will be an additionalm1+m2+m3
columns for the artificial variables introduced to solve the first phase of the problem.  basic

The indices of the basic (nonzero) variables in the solution. Indices between
n+1
andn+m1
correspond to slack variables, those betweenn+m1+1
andn+m2
correspond to surplus variables and those greater thann+m2
are artificial variables. Indices greater thann+m2
should occur only ifsolved
is1
as the artificial variables are discarded in the second stage of the simplex method.  slack

The final values of the
m1
slack variables which arise when the "<=" constraints are reexpressed as the equalitiesA1%*%x + slack = b1
.  surplus

The final values of the
m2
surplus variables which arise when the "<=" constraints are reexpressed as the equalitiesA2%*%x  surplus = b2
.  artificial

This is NULL if a feasible solution can be found. If no solution can be found then this contains the values of the
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.