Answer :
Final answer:
The statement is true as there are some instances, especially when the number of unknowns exceeds the number of equations, where a solver cannot solve integer programming problems even if they possess an optimal solution.
Explanation:
The statement is true. There are some integer programming problems that a solver may be unable to solve, even when they have an optimal solution. This is particularly the case when the number of unknowns is larger than the number of equations. For example, consider a system of two equations with three unknowns. This system can have multiple solutions or none at all, making it difficult for a solver to identify a single optimal solution, thus making the problem unsolvable by a solver.
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