6. (15%) Suppose x units of labor and y units of capital are required to produce

f(x, y) = 100x^3/4y^1/4
units of a certain product. If each unit of labor costs $200 and each unit of capital costs $300 and a total of $60,000 is available for production, determine how many units of labor and how many units of capital should be used to maximize production.

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