Answer the following questions, continuing to assume the production function for DurableTires Corp. is Q=L^1/3K^1/2, where Q is the quantity of tires produced, L is the number of workers employed, and K is the number of machines rented. Moreover, assume the wage per unit of labor (wL) is $50 and the rental price per machine is $200 (wK). 

a. What is the total cost of producing the quantity of tires you found in your answer to question (5-23)? And the average cost? Assuming the number of machines rented does not change, what is the marginal cost of producing one additional tire? 

b. Given the production function above, the marginal product of labor and the marginal product of capital are MPL= 1/3(L^-2/3K^1/2) and MPK=1/2(L^1/3K^-1/2), respectively. Given the wage and rental rate above, is DurableTires Corp. adopting an optimal input mix to produce the quantity of tires found in question (5-23a)? If yes, why? If not, why not, and how could DurableTires Corp. save money producing that same quantity of tires? Explain. 

c. What happens to the optimal input mix you found in question (5-23) if the government introduces a tax that raises the cost of labor to $150 per worker? Explain.