A firm uses inputs of labor, L, and capital, K, to produce its output, Q, according

to the production function: = (, ) = 91/31/3. The firm is a price-taker in the input

markets. Labor is paid an hourly wage of w = 12$, and the price of capital is r = 6$. The firm

sells its output at a price of p = 4$ per unit.

a) Maximize the profit function to determine the optimum level of each input the firm

should use.

b) Check second-order sufficient condition.