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If the assumptions we typically have on preferences and utility hold (completeness, transitivity, and monotonically increasing), an individual who solves a utility maximization problem will
choose the consumption bundle lying on the highest indifference curve that he can attain given his budget constraint.
choose the most balanced bundle that he can afford.
choose any bundle in his budget constraint, because they all give him the same utility.
choose the consumption bundle lying on the indifference curve that is closest to the origin.