4. (20 points) Suppose that a firm's production technology is described by the production function f(x1, x2) = (x1) 2x2, where x1 denotes the quantity of input 1 and x2 denotes the quantity of input 2. Let the price of input 1 be $1 and the price of input 2 be $4. 2 a. (10 points) Derive the conditional input demand functions for both inputs. b. (10 points) Derive the firm's cost function.