Class of objects that result from solving a linear programming
problem using `simplex`

.

This class of objects is returned from calls to the function `simplex`

.

The class `"saddle.distn"`

has a method for the function `print`

.

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 of`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`1`

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 re-expressed such that the basic variables have coefficient zero.

- a.aux
This is

`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.- 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

`m1+m2+m3`

by`n+m1+m2`

, where the final`m1+m2`

columns correspond to slack and surplus variables. If no feasible solution is found there will be an additional`m1+m2+m3`

columns for the artificial variables introduced to solve the first phase of the problem.- basic
The indices of the basic (non-zero) variables in the solution. Indices between

`n+1`

and`n+m1`

correspond to slack variables, those between`n+m1+1`

and`n+m2`

correspond to surplus variables and those greater than`n+m2`

are artificial variables. Indices greater than`n+m2`

should occur only if`solved`

is`-1`

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 re-expressed as the equalities`A1%*%x + slack = b1`

.- surplus
The final values of the

`m2`

surplus variables which arise when the "<=" constraints are re-expressed as the equalities`A2%*%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.