Consider a firm which employs two inputs x1 and x2 to produce a single final output y. Suppose this firm's technology is best characterized by the following production function y = 6x 1/3 1 x 1/3 2.where x1 and x2 are the amount of input 1 and input 2 employed by the firm. Furthermore, assume the price of the final good is p = $3, the input price of x1 is w1 = $8 and the input price of x2 is w2 = $4. The firm is making long-run decisions about the optimal choice of inputs to employ and the number of products to make.

Derive the short-run profit-maximizing input demands (x 1 , x 2 ) for the firm.