> I see, I'll try to call mip status instead. 
> 
> But it doesn't explain why the lp relaxation status is GLP_OPT,
> clearly lp relaxation is infeasible.

You may write your instance to a text file in human-readable format with
glp_write_lp, solve it with glpsol, and check the solution.

> 
> Does GLPK add something like 0*continuous_variable when all integers
> are indicated?
> 

No, it doesn't. However, internally for each row glpk introduces one
auxiliary variable (similar to slack) which is continuous. For more
details please see the glpk reference manual, Chapter "Advanced API
Routines", Section "Background".



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