A firm has the following production function, Q = Q(K,L) = K²+L², where Q is output, and K (capital) and L (labour) are inputs. 9. The firm's costs are given by: C = wL +rK , where w is the price of labour and r is the price of capital. The price of the output is P. (a) Maximise the firm's profits and thus find the input demand functions. These will be expressed in terms of P, w, and r. (b) Ensure that the optimal point found in (a) is a maximum. (c) Express the optimal output in terms of P, w, and r.

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