For minimization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?

A lower bound on the optimal integer value.

Explanation:

The question is poorly typed.  The original question requires the optimal solution of the objective function of a minimization problem

I will answer this question base on the above illustration.

When an objective function is to be minimized, it means that the objective function will take the feasible solution with the least value.

The least value are often referred to as the lower bound.

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