Problem 2. lConsider the production of widgets, which are produced using labor {L} and capital (K). The production function for widgets is given by: q = f(L_.K) : 314% (i The wage rate is $10 and the rental rate is $40. (2.1] What are the quantities L' and K ' that produce 300 widgets at minimum cost? (2.2] Suppose in the short r1111 L can be adjusted but K is xed at the K' level you found above. What is the level of L required to produce 600 widgets in the short run? {2.3) With L on the horizontal axis and K on the vertical axis, show your solutions to (2.1) and (2.2} above in a graph. Include the relevant isoquants, isocosts.. and label the input bundles. Include the short term expansion path {the path of (L, K} points the rm hires as the quantity produced changes in the short run}. {2.4) Derive the short-run total cost function TC(q} as a function of the quantity of widgets q produced