constrained, parametric optimization

I am developing a computer program which needs to solve a constrained,
parametric optimization, something like :

meaning to calculate min(x) such as y = b*x+a and x <= c and x >=0
where x and y are variables, a, b, c are constant but unknown parameters.
Since the problem is calculated at runtime from my computer program and
changes every time, I think I need to solve it with some form of constrained
programming with a symbolic result.

I could see something like this in mathematica :

http://reference.wolfram.com/mathematica/ref/Minimize.html#61381153

but I would like to keep my program free and open source, so I would like to
use a free library for this...

could you please tell me if I can do this using axiom?
thank you very much in advance!
Luca

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