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If an LP problem has alternate optimal solutions, do they provide the same objective value?

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Yes, alternate optimal solutions always yield the exact same optimal objective value. They represent different point combinations along a feasible boundary that all produce identical performance.

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Yes. Alternate optimal solutions have different decision-variable values but the same optimal objective value.

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If an LP problem has alternate optimal solutions, all of those solutions provide the same optimal objective value, even though the values of the decision variables may be different.

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