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.
- $$f ( x , y , z ) = ( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z - 4 ) ^ { 2 } , x - y + 3 z = 7$$

A) Maximum: none; minimum: $\frac { 64 } { 11 }$ at $\left( \frac { 14 } { 11 } , - \frac { 3 } { 11 } , \frac { 20 } { 11 } \right)$
B) Maximum: none; minimum: $\frac { 188 } { 11 }$ at $\left( - \frac { 14 } { 11 } , \frac { 3 } { 11 } , \frac { 20 } { 11 } \right)$
C) Maximum: none; minimum: $\frac { 76 } { 11 }$ at $\left( \frac { 14 } { 11 } , \frac { 3 } { 11 } , \frac { 20 } { 11 } \right)$
D) Maximum: none; minimum: 36 at $\left( \frac { 14 } { 11 } , \frac { 3 } { 11 } , - \frac { 20 } { 11 } \right)$