## Version 1.2.0

31 January 2011

Recent Changes

This package uses the simplex method to solve the linear programming problem $\text{minimize } \mathbf {c} ^T \mathbf{ x} = \sum_{ j=1} ^ n c _j x _j$ subject to the constraints \begin{aligned} &\mathbf {Ax} = \mathbf {b}, \; \text{that is,} \; \sum_{ j=1} ^ n a _{ij} x _j = b _i, \; i = 1, 2, ... m \\ &l _j \le x _j \le u _j, \; 1 \le j \le k, \\ &\qquad x _j \ge 0, \quad l \le j \le n.\end{aligned}
The variables $$x _j$$, $$k+1 \le j \le l-1$$, if any, are free (have no bounds). Full advantage is taken of any zero coefficients $$a _ {ij}$$. The inequalities $$0 \le k < l \le n+1$$ must hold. Special values $$l _i = - \sigma$$ and $$u _i = \sigma$$ may be used to remove one or both bounds.