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= 6LMPL= 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?
2. Given the firm's $300,000 budget, how much capital and labor should the firm employ? How much output will the firm produce?
3. The state is planning to increase the minimum wage from $7.50 an hour to $15 an hour. 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?