A firm has the following production function where q represents the output level per week, L represents the number of hours of labor the company uses in a week, and K represents the number of machine-hours the company uses in a week: q = 41025 0.25 The hourly price of capital is denoted by r, and the hourly price of labor is denoted by w. 1) Solve the firm's cost minimization problem and find optimal L* and K* levels as a function of q, w, and r. [8pts] For questions (2)-(4), assume w=4 and r=1. 2) Assume the firm wants to produce 16 units this week (q=16). How many hours of labor and capital should the firm's company hire? How much will it cost to produce those 16 units? [4 pts] 3) Assume that the firm is in the long run (that is, the firm can adjust L and K). What is the firm's supply curve? [4pts] 4) Suppose now that the firm decides to produce 40 units instead. However, the firm has already hired 32 hours of machines and cannot adjust K. The firm can only adjust the hours of labor, L, (that is, the firm is in the short run). How many units of labor will the firm hire? How much will it cost to meet this new production level? [4pts]