2. (16 marks) Suppose a rm has the production function f (L, K) = L + 2K: The output price is p. The prices of capital and labor are r and w, respectively. (a) Find the cost minimizing Land Kas functions of r and w. Suppose r not equal to 2w. (b) Assume the prices are p = 12; w = 15 and r = 10: Suppose the rm has a capacity constraint: it can produce at most 100 units. Find the prot maximizing quantity, and input combination. Find the prot level? 3. (24 marks) Suppose a rm has the production function f (L, K) =K 1'4 L 1'2. The output price is p. The prices of capital and labor are r and w, respectively. (a) Find the prot maximizing input demands K (p, r, w) and L (p, r, w). (b) Find the prot maximizing output q and prot in terms of p, r and w. (c) Law of Output Supply states that the output supply is increasing in output price, and Law of Input Demand states that input demands K (p, r, w) and L (p, r, w) are decreasing in their own prices, r and w respectively? Are your answers consistent with the Law of Output Supply and Law of Input Demand? Explain