For many years my specialization in the enterprise was to optimize systems. We used many packages, up to including ones that dealt with very large problems of hundreds of thousands of variables. Problems like those need special techniques and fast computers.
I have just been connected to some smaller problems and was reminded of a vendor called Lindo Systems, which we used in the enterprise many times. I am happy to endorse them, especially for small to medium size problems. They are well known for their Whats Best! system, which can be connected to Excel to solve both linear and non-linear problems. They have a number of other math programming packages to suit your needs. You can download any of their packages free and try them with limited problem sizes.
Especially useful is their library of applications which looks at many kinds of solutions you can tailor to your problem.
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