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Optimization

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If a company has m hours of machine time and w hours of labor, it can produce 3m^(1/3)w^(2/3) units of a product. Currently, the company has 216 hours of machine time and 1,000 hours of labor. An extra hour of machine time costs
$100, and an extra hour of labor costs $50. If the company has $100 to invest in purchasing additional labor and machine time, would it be better off buying I hour of machine time or 2 hours of labor?

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