Let F(x, Y, Z) = Xyz

Short Answer

Let f(x, y, z) = xyz. Find the point(s) where f(x, y, z) may have a possible relative maximum or minimum, subject to the constraint x + 6y + 3z = 36 and where x > 0, y > 0, z > 0. Use the method of Lagrange multipliers.
Enter your answer as just (a, b, c) where a, b, c are all integers.