Find the Extreme Values of the Function Subject to the Given

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y , z ) = x + y + z , \frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = 1$$

A) Maximum: 9 at (3, 3, 3) ; minimum: 3 at (1, 1, 1)
B) Maximum: 11 at (6, 3, 2) , (6, 2, 3) , (3, 2, 6) , (3, 6, 2) , (2, 3, 6) , (2, 6, 3) ; minimum: 1 at (1, 1, -1) , (1, -1, 1) , (-1, 1, 1)
C) Maximum: 6 at (2, 2, 2) ; minimum: -3 at (-1, -1, -1)
D) Maximum: 6 at (2, 2, 2) ; minimum: 3 at (1, 1, 1)