A firm's profits, , depend on the quantity of capital, K and labour, L, that it hires, according to the following expression = K ^1/4L ^1/4 rK wL, where r is the rental rate of capital and w is the wage rate.

a) Find expressions for the values of K and L that maximize profits, as functions of the rental rate of capital and the wage rate.

(b) Verify that the second-order conditions for a maximum are satisfied.