A perfectly competitive firm hires its machines at a constant rental rate of r = 5 euros per unit and its workers at a constant wage rate of w = 4 euros per unit. It can also sell as much output as it wishes at the ruling market price of P = 40 euros. The firm's production function is given by: Q = K^{0.25 }L^{0.5}
where L is labour and K is capital.
(a) If the firm wishes to maximise profits, write down the constrained maximum problem that the firm faces.
(b) Determine the profit maximising levels of capital, labour and output.