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Afair, lpsolve had both C api (you may find it horrible) and dsl. http://lpsolve.sourceforge.net/5.5/

There are few web/node-based, but I assume you googled them already.



lp_solve and coinOR project's CBC are free/open source and can bind to C or C++.

They also are released as binary executables that can be called from the command line or Excel.




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