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Consider a perfectty competitive rm which produces hoclteg,r sticks using capital (K) and labour {L}. The production function is given by q = K\"? + L132. The per-unit oosts ofKand L are t! and to. (a) Consider the frrm's decision over K and L as a prot-maximizing problem and compute: (i) the factor demand functions for both K and L and (ii) the supply' function. ('10 marks) {b} Consider the rm's decision over K and L 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. (3 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 supplyr function from part a}. (6 marks}