Maximize F(x, Y, Z) = X + Y + Z $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1 , x , y , z > 0$

Short Answer

Maximize f(x, y, z) = x + y + z subject to the constraint $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1 , x , y , z > 0$ Enter your answer as just $3 ^a$ where a is a reduced fraction of form $\frac { b } { c }$ .