You are the manager for Herman Miller, a major manufacturer of office furniture. You recently hired an economist to work with the engineering and operation experts to estimate the production function for a particular line of office chairs. The relevant production function is Q = 6KL, where Q represents the annual chair production, K represents capital equipment, and L is the number of labor hours worked per year. The marginal products of capital and labor are given as follows: MPK = 6L MPL = 6K Workers at the firm are paid a competitive wage of $7.50 per hour. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and labor is $300,000 per year.

1. What is the firm's optimal ratio of labor to capital? Given the firm's $300,000 budget, how much capital and labor should the firm employ? How much output will the firm produce?

2. The state is planning to increase the minimum wage from $7.50 an hour to $15 an hour.

3. Assuming that the firm intends to maintain its pre-increase in minimum wage output, how much capital and labor should the firm employ? What happens to the firm's cost as a result of the the increase in minimum wage?