A firm produces an output y using labor and capital, whose quantities are denoted respectively by x_L and x_K. Suppose this firm's production function is given by
f(L, K) = 50\sqrt{KL}+K+L.
Answer the following questions.
a. Derive the marginal product of labor and the marginal product of capital.
b. Is the marginal product of labor diminishing everywhere? Does it ever take negative values?
c. Does the production process of this firm exhibit increasing, constant, or decreasing returns to scale?