Solve the Given Problem by Using Substitution $f ( x , y , z ) = 8 - x ^ { 2 } - y ^ { 2 } - z ^ { 2 }$

Solve the given problem by using substitution.
Find the maximum value of $f ( x , y , z ) = 8 - x ^ { 2 } - y ^ { 2 } - z ^ { 2 }$ subject to $z = 3 y$ .

A) $f _ { \max } = 8$
B) $f _ { \max } = 9$
C) $f _ { \max } = 3$
D) $f _ { \max } = 10$
E) $f _ { \max } = 7$

Correct Answer:

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