. Consider the same production function as in problem 1 (a), which is Q = L^1/4K^3/4 . a. For general w and r, derive the conditional input demand functions for L and K using the Lagrangian method. b. Find the combination of inputs that minimizes the cost of producing 1000 units of output for w = $1 and r = $4. c. Graph your result on a isoquant-isocost diagram. d. Is the demand for labour downward sloping? Is the demand for capital downward sloping? Use calculus to answer.