why should people trust free software?

[Andrew Makhorin]

Hi,

I am the author and maintainer of glpk (a GNU package for linear
programming). Recently I received a question from a user of glpk that
touches an important issue (as seems to me) concerning free software.
Here is it:

>I am doing this job for a company, and I would like to advocate free
>software for them. As I see it, the problem I will face is with
>trust. They simply trust proprietary software because it costs money
>and a company is responsible. To make this selling-task feasible, I
>would like to get some data from you that puts trust into glpk. 
>
>Anything that puts trustworthyness (sp?) into glpk. Can you help me
>with this? I have a golden opportunity, since I will be working with
>upper management... :) I don't think they'll install Debian right
>away, but this is at least a start.

Could anyone give necessary comments to this question?

Thank you,

Andrew Makhorin,
the author and maintainer of GLPK