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A determine the firms optimal capital-labor ratio given the

Davy Metal Company has the following production function:

Q = 500L^0.6K^0.8,

MPL = 300L^-0.4K^0.8

MPK = 400L^0.6K^-0.2

Employees earn $15 per hour. Rental charge is$50 per hour on capital. Davy forecasts annual costs of $500,000 per year.

a. Determine the firm's optimal capital-labor ratio, given the information above.

b. How much capital and labor should the firm employ, given the $500,000 budget? Calculate the firm'soutput. Please show all steps.

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