1. Heavy Metal Company produces brass fittings.Heavy Metal's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions. Q = 5KL,

where Q = annual output,

L = labor measured in person hours,

K = capital measured in machine hours.

The marginal products of labor and capital are:

MPL = 5K MPK = 5L

Heavy Metal's employees earn $25 per hour. The firm estimates a rental charge of $50 per hour on capital.Heavy Metal forecasts annual costs of $100,000 per year, measured in real dollars.

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 $150,000 budget?

c. Calculate the firm's output.

d. Suppose now the firm sets a target output of 8000. What would be the cost-minimizing allocation of capital and labor for the firm?