A farmer can produce f (x, y) = 200√6x² + y² units of produce by utilizing x units of labor and y units of capital. (The capital is used to rent or purchase land, materials, and equipment.)

(a) Calculate the marginal productivities of labor and capital when x = 10 and y = 5.

(b) Let h be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from 10 to 10 + h units while keeping capital fixed at 5 units.

(c) Use part (b) to estimate the change in production when labor decreases from 10 to 9.5 units and capital stays fixed at 5 units.