Problem 2. Consider a firm using capital (K} and labour (L) according to a generic produc- tion function Y(K:L). Assume all markets are perfectly competitive (i.e., the labour market, the capital market and the product market). Let w be the prevailing wage rate and r the cost of renting capital. The firm sells its product at the market price P. Derive the optimality conditions for the maximisation of profits when the firm can adjust both labour and capital