A manufacturer of automobile batteries estimates that his total production (in thousands of units) is given by ƒ(x, y) = 3x^1/3y^2/3, where x is the number of units of labor and y is the number of units of capital utilized.
(a) Find and interpret ƒ_x(64, 125) and ƒ_y(64, 125)  if the current level of production uses 64 units of labor and 125 units of capital.

(b) Use your answer from part (a) to calculate the approximate effect on production of increasing labor to 65 units while holding capital at the current level.
(c) Suppose that sales have been good and management wants to increase either capital or labor by 1 unit. Which option would result in a larger increase in production?