1. Solve (mixed integer) linear programming problems The linear programming (LP) problem can be formulated as: Solve A.x >= V1, with V2.x maximal. A is a matrix, x a vector of (nonnegative) variables, V1 a vector called the right hand side, and V2 a vector specifying the objective function. An integer linear programming (ILP) problem is an LP with the constraint that all the variables are integers. In a mixed integer linear programming (MILP) problem, some of the variables are integer and others are real. The program lp_solve solves LP, ILP, and MILP problems. It is slightly more general than suggested above, in that every row of A (specifying one constraint) can have its own (in)equality, <=, >= or =. The result specifies values for all variables. lp_solve uses the 'Simplex' algorithm and sparse matrix methods for pure LP problems. If one or more of the variables is declared integer, the Simplex algorithm is iterated with a branch and bound algorithm, until the desired optimal solution is found. lp_solve can read MPS format input files. From Debian 3.0r0 APT