Suppose that the total cost (in dollars) of producing a product is C(x, y) = 25 + 2x2 + 3y2, where x is the cost per pound for material and y is the cost per hour for labor.
(a) If material costs are held constant, at what rate will the total cost increase for each $1-per-hour increase in labor?
(b) If the labor costs are held constant, at what rate will the total cost increase for each increase of $1 in material cost?