Castro's daily production function for producing custom-printed mugs is q = 15K^0.5L^0.5. The price of labor is $40 and the price of capital is $10. a. Find and sketch the expansion path. b. How much capital and labor should Castro employ to produce 150 mugs a day? c. What is the lowest possible cost of producing 150 mugs a day? d. Repeat parts (b) and (c), for an output level of 450 mugs. e. What is the firm's LRAC at q = 150? At q = 450? What does the firm's LRAC look like over this range of output? Are there economies of scale? Explain