somebody claims that linear programming (lp) is not significantly different from integer linear programming (ilp), even though in the latter the additional requirement is included that the variables can only take integer values. after all, he argues, one can always ignore the requirement that the variables are integers, and then solve the task as linear programming. at the end, if needed, one can always round the non-integer values to the nearest integer, it does not make any significant practical difference. what is wrong with this argument?