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Name
    Algorithm::Simplex - Simplex Algorithm Implementation using Tucker
    Tableaux

Synopsis
    Given a linear program formulated as a Tucker tableau, a 2D matrix or
    ArrayRef[ArrayRef] in Perl, seek an optimal solution.

        use Algorithm::Simplex::Rational;
        my $matrix = [
            [ 5,  2,  30],
            [ 3,  4,  20],
            [10,  8,   0],
        ];
        my $tableau = Algorithm::Simplex::Rational->new( tableau => $matrix );
        $tableau->solve;
        my ($primal_solution, $dual_solution) = $tableau->current_solution;

Methods
  _build_number_of_rows
    Set the number of rows. This number represent the number of rows of the
    coefficient matrix. It is one less than the full tableau.

  _build_number_of_columns
    Set the number of columns given the tableau matrix. This number
    represent the number of columns of the coefficient matrix.

  _build_x_variables
    Set x variable names for the given tableau, x1, x2 ... xn These are the
    decision variables of the maximization problem. The maximization problem
    is read horizontally in a Tucker tableau.

  _build_y_variables
    Set y variable names for the given tableau. These are the slack
    variables of the maximization problem.

  _build_u_variables
    Set u variable names for the given tableau. These are the slack
    variables of the minimization problem.

  _build_v_variables
    Set v variable names for the given tableau: v1, v2 ... vm These are the
    decision variables for the minimization problem. The minimization
    problem is read horizontally in a Tucker tableau.

  get_bland_number_for
    Given a column number (which represents a u variable) build the bland
    number from the generic variable name.

  determine_bland_pivot_column_number
    Find the pivot column using Bland ordering technique to prevent cycles.

  determine_bland_pivot_row_number
    Find the pivot row using Bland ordering technique to prevent cycles.

  min_index
    Determine the index of the element with minimal value. Used when finding
    bland pivots.

  exchange_pivot_variables
    Exchange the variables when a pivot is done. The method pivot() does the
    algrebra while this method does the variable swapping, and thus tracking
    of what variables take on non-zero values. This is needed to accurately
    report an optimal solution.

  get_row_and_column_numbers