You can prefer LİNDO very easy comparing with GAMS

Thanks sir

I don't know in GAMS but in Solver it means that there is no optimal solution for that problem, and consequently, it is not feasible, at least from the point of view of finding a solution with integer values. Probably it is feasible with decimal values

I hope you have been able to solve your problem. A few tutorial notes might be helpful for this --- a feasible integer solution is one that satisfies all the constraints and is integer. Assuming there are lots of feasible solution values, the optimal solution is the best over the feasible set. Clearly, you cannot discuss optimality without having possession of some feasible solutions. No feasible solution => no optimal solution.

How do we get in-feasibility? It occurs because of inconsistent constraints. If you believe there should be a feasible solution, you have to check your formulation. This usually arises with a typo in the formulation or an error in signs on some aspect of a constraint. If the formulation is very experimental and you are sure it is correct, it might actually be useful to know that there are incompatibilities between your constraints. For example, if you constrain

X>2 and X

is your problem in such a form that a trivial feasible solution can be identified by inspection and you just set var = val and see if you get the same error?

Often people are sure that the more in GAMS represents their model but somewhere some indices are wrong or something that makes the gams model different from what they believe it should be. I personally, often export LP ou MPS file and check it. If that really tells what I wanted to tell. and it helps.

I support Morton O'Kelly very rational and clear comment.

Obviously, if there is no a feasible solution, contained in the polytope, there is no way that an optimal solution could exists since it should be in one of the corners of the polytope.

The example that he puts is very realistic, it is obvious that a solution can't be at the same time higher than a maximum value and lower than a minimum one, and this translates that this condition does not exist in the polytope, and then is unfeasible, and this is valid for integer and not integer values. However, a solution that is larger that a minimum and lower than a maximum, may exist as feasible. For instance ,you want to keep a minimum of your stock of a certain product, but at the same time, you want that the consumption be less than a maximum