A competitive firm produces output y using two inputs, labour L and capital K. The firm faces a product price p and input prices w and r per unit, and has production function y - AL"K", where a, B > 0. (a) Characterize the optimal inputs using the first order conditions. (b) What further restrictions on or and B can we make to ensure that gives a maximum? (c) Let y = [0.20.6, p = 100, w = 10, and r = 20. Solve for L* and A* and show that this is in fact a true optimum