A firm faces the production function = 2 ^0.2 ^0.6 (where K is capital and L is labor) and can buy L at $240 a unit and K at $4 a unit.

] a) Find an expression for the marginal product of capital. [1] b) Find an expression for the marginal product of labor. [3] c) Find the second-order partial derivatives, provide an economic interpretation of the results. [2] d) Find the cross-order partial derivatives, provide an economic interpretation of the results. [1] e) If the firm has a budget of $16,000, what is its total cost function? [1] f) What is the Lagrange function if the firm aims to maximize its output? [6] g) What combination of K and L should it use to maximize output?