Solve the Given Problem by Using Substitution $f ( x , y , z ) = 3 - x ^ { 2 } - x - y ^ { 2 } + y - z ^ { 2 } + z$

Multiple Choice

Solve the given problem by using substitution.
Find the maximum value of $f ( x , y , z ) = 3 - x ^ { 2 } - x - y ^ { 2 } + y - z ^ { 2 } + z$ subject to $y = 3 x$ .

A) $f _ { \max } = 3.225$
B) $f _ { \max } = 3$
C) $f _ { \max } = 3.35$
D) $f _ { \max } = 2.775$
E) $f _ { \max } = 2.45$