> If in optimal solution c is expected to take on value a or b,

More precisely, if removing the constraint c = min(a, b) leads to 
c > min(a, b) in optimal solution, for example, if c has to be
maximized.

>  you can
> replace the constraint c = min(a, b) with the following two linear
> inequality constraints:
> 
> c <= a
> c <= b



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