Let $w = ( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z + 1 ) ^ { 2 }$

Multiple Choice

Let $w = ( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z + 1 ) ^ { 2 }$ with constraint $x + 4 y + 3 z = 2$ . Then the minimum value of w is

A) $\frac { 37 } { 13 }$
B) $\frac { 35 } { 13 }$
C) $\frac { 33 } { 13 }$
D) $\frac { 32 } { 13 }$
E) $\frac { 30 } { 13 }$