Let $w = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$

Multiple Choice

Let $w = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ with constraint $9 x ^ { 2 } + 4 y ^ { 2 } + z ^ { 2 } = 36$ . Then the maximum value of w is

A) 48
B) 40
C) 36
D) 32
E) 28