Consider a perfectly competitive firm which produces hockey sticks using capital (K) and labour (L). The production function is given by q = K 1/2 + L 112. The per-unit costs of K and L are u and w. (a) Consider the firm's decision over K and Las a profit-maximizing problem and compute: (1) the factor demand functions for both K and L and (ii ) the supply function. (10 marks) (b) Consider the firm's decision over K and I as a cost-minimizing problem under the constraint that a certain output level be produced and compute the conditional or output- constant factor demand functions for both K and L. (8 marks) (c) Using the conditional factor demand functions derived in part (b), compute the long-run cost function and supply function (NOTE: the supply function from part c should be identical to the supply function from part a). (6 marks)