8. The firm estimates its production function to be Q = 6LK; where O = annual paper production measured in pounds, output measured in pounds. K = machine hours of capital, and _ = labor measured in person hours. Workers earn $7.50 an hour and the rental rate of capital is estimated to be $30 per hour. The firm has an operating budget of $300,000 per year. a. Write out the firm's optimization problem. b. Determine the firm's optimal labor to capital ratio. c. Given the firm's $300,000 budget, how much capital and waste water should the firm employ? d. How much output will the firm produce? e. The labor union has successfully negotiated a wage increase of $7.50 per hour. If the firm intends to maintain is output in part c, how much capital and labor should the firm employ? f. How much will the firm pay in labor costs? g. What happens to the firm's cost because of the new wage structure? h. Is this an increasing, decreasing or constant return to scale production function? Explain