Since the number of feasible solutions to a pure integer programming problem is a lot less than the number of feasible solutions to the corresponding linear programming problem (i.e. problem obtained by ignoring the integrality constraints), a pure integer programming problem must be easier to solve.

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Although the number of feasible solutions to a pure integer programming problem is indeed less than that of the corresponding linear programming problem, the process of finding the optimal solution among integers is more complex due to the discrete nature of the solutions. This makes integer programming problems generally harder to solve than their linear programming counterparts.

Since the Number of Feasible Solutions to a Pure Integer