A price taking firm employs two inputs, capital (K) and labor (L). Input prices are a follows. The rental rate for capital, r, is $4. The wage for labor, w, is $5. The firm can sell output at a price of p = $10 per unit. The firm’s production function is given by:

The firm wants to maximize profit.

A. Write down the profit function of the firm.

B. Write down the first order conditions and from these conditions the quantities of each input.

C. Verify that the quantities you have found in part (B) are indeed (globally) optimal.