Please help with this question. Thank you!

Q2 (20 points) A firm has a Cobb-Douglas production as follows: F(L, K) = (LK)\"4 For this question, you do not need to consider the possibility of shutting down. ** Part a (5 marks) Show that the production function is exhibiting diminishing marginal product of Labor. (Hint: first find the marginal product of labor and then show that it is decreasing in L). ** Part b (5 marks) Suppose that K is fixed at I_( = 1. Suppose thatp = 1, w = 1, r = 1. Find the L in the short-run given q as L(q). ** Part c (5 marks) Following Part b, find the short-run cost function. ** Part d (5 marks) Now consider the long-run where K is not fixed. Find the long-run cost function