Employees earn 15 per hour rental charge is50 per hour on

Question

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'soptimal 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.