3) Derive the profit function for a perfectly competitive firm if its production function is given by f(L,K) = L1/4K1/2. a) Does the chosen combination of L and K profit maximizing? Verify using the second order conditions b What is the degree of homogeneity of the profit function? C) Also derive firm's conditional input demand functions if the output is 200. d) Suppose w = 9 and r = 1. P = 5. Does the optimal number of L and K differ depending on whether you use the conditional input demand functions or unconditional ones? Why? e ) Verify Hotelling's lemma for this firm