AMPL: A Modeling Language for Mathematical Programming
In my quest to get some calculations done, as it seems my math knowledge is less than good enough, I have had to resort to use other tools I can handle. Serendipity led me to AMPL language developed at Bell Labs (by Brian W. Kernighan et al.).
AMPL is used by Operations Research practitioners to solve Linear Programming problems. But the fact that AMPL is mostly a language to express math problems does not mean it can solve them. If you have a LP problem you can express it using AMPL but you need a solver to actually solve the problem. AMPL can work with may different solvers (some free others are commercial) and the solver you use may also depend on the nature of your problem. For example, your LP problem might have non-linear constraints that some solvers can't deal with.
You can download a free student version of AMPL. You can also obtain different solvers and I am using the free student version of LOQO solver by Princeton's Robert Vanderbei. Another possible choice, without the need of installing any software, is to use the on-line version at NEOS Server, where you can chose among a wide selection of solvers.
But if you do not feel comfortable with commercial software and/or do not want to pay for the uncrippled version there is some hope as GLPK is a subset of AMPL and it is free software. Unfortunately GLPK does not handle the non-linear constraints of my problem yet.