### How many labor hours and machine hours should firm employ

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Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions. Q = 500L^0.6K^0.8 where Q = annual output measured in pounds, L = labor measured in person hours, K = capital measured in machine hours. Davy's employees are relatively highly skilled and earn \$15 per hour. The firm estimates a rental charge of \$50 per hour on capital. Davy forecasts annual costs of \$350,000. a. How many labor hours and machine hours should the firm employ, given the \$350,000 budget?

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