## `linopt::Transparent::result` -- get the basic feasible solution belonging to the given simplex tableau

#### Introduction

`linopt::Transparent::result(`tableau`)` returns the basic feasible solution belonging to the given simplex tableau `tableau`.

#### Call(s)

`linopt::Transparent::result(tableau)`

#### Parameters

`tableau` | - | a simplex tableau of domain type `linopt::Transparent`

#### Returns

a set containing the values of the user defined variables for the feasible solution.

#### Related Functions

`linopt::Transparent`, `linopt::Transparent::dual_prices`

#### Details

- This procedure returns the basic feasible solution belonging to the given tableau in form of a set of equations. Only the user defined variables are taken into account - the dual prices can be achieved by use of `linopt::Transparent::dual_prices`.

#### Example 1

We first compute an edge for an initial simplex tableau:

    >> k := [[x <= 1, y <= 1, x + y >= 2], 0, NonNegative]:
       t := linopt::Transparent(k):
       linopt::Transparent::result(t)

                                  {x = 0, y = 0}

Now we compute the edge for the final tableau, which is identical to the optimal solution of the linear program given by `k`. We get the final simplex tableau by using `linopt::Transparent::simplex`:

    >> t := linopt::Transparent(k):
       t := linopt::Transparent::simplex(t):
       linopt::Transparent::result(t)

                                  {x = 1, y = 1}

    >> linopt::minimize(k)

                           [OPTIMAL, {x = 1, y = 1}, 0]

    >> delete k, t:

#### Background

- References:

  Papadimitriou, Christos H; Steiglitz, Kenneth: Combinatorial Optimization; Algorithms and Complexity. Prentice-Hall, 1982.

  Nemhauser, George L; Wolsey, Laurence A: Integer and Combinatorial Optimization. New York, Wiley, 1988.

  Salkin, Harvey M; Mathur, Kamlesh: Foundations of Integer Programming. North-Holland, 1989.

  Neumann, Klaus; Morlock, Martin: Operations-Research. Munich, Hanser, 1993.

  Duerr, Walter; Kleibohm, Klaus: Operations Research; Lineare Modelle und ihre Anwendungen. Munich, Hanser, 1992.

  Suhl, Uwe H: MOPS - Mathematical OPtimization System. European Journal of Operational Research 72(1994)312-322. North-Holland, 1994.

  Suhl, Uwe H; Szymanski, Ralf: Supernode Processing of Mixed Integer Models. Boston, Kluwer Academic Publishers, 1994.

#### Changes

- new function
- The linopt library was completely rewritten in MuPAD version 2.0.

Do you have questions or comments?
Copyright © SciFace Software GmbH & Co. KG 2000