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3. A firm's production function is given by Q = 21 1/2 + 31 1/2 where Q, L and K denote the number of units of output, labour and capital, respectively. Labour costs are $2 per unit, capital costs are $1 per unit and output sells at $8 per unit. If the firm is prepared to spend $99 on input costs, find the maximum profit and the values of K and L at which it is achieved