Yes, it is possible, though I can only think of one non-trivial example. IF your solution set were restricted to the integers, then a result that looked like:
Would have the single element 4 in the solution set.
This is not really that far-fetched either. Modeling of real-world situations frequently requires that the solution be restricted to the integers. For example, the problem of how many of a particular product to manufacture so that you either maximize profit or minimize cost based on various types of resource constraints. If you were building refrigerators, it wouldn't make much sense to make a fractional part of a refrigerator. So the answer would have to be a whole number of refrigerators.
