Use Lagrange Multipliers to Minimize the Function $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$

Multiple Choice

Use Lagrange multipliers to minimize the function $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ subject to the following constraint. $x + y + z - 21 = 0$ Assume that x, y, and z are positive.

A) 49
B) 147
C) 98
D) 294
E) 441