Solve the Given Problem by Using Substitution $S = x y + x z + y z$

Solve the given problem by using substitution.
Minimize $S = x y + x z + y z$ subject to $x y z = 5$ with $x > 0$ , $y > 0$ , $z > 0$ .

A) $S _ { \min } = 3 \left( 5 ^ { \frac { 2 } { 3 } } \right)$
B) $S _ { \min } = 3 \left( 6 ^ { \frac { 2 } { 3 } } \right)$
C) $S _ { \min } = 3 \left( 4 ^ { \frac { 2 } { 3 } } \right)$
D) $S _ { \min } = 3 \left( 5 ^ { \frac { 1 } { 3 } } \right)$
E) $S _ { \min } = 3 \left( 6 ^ { \frac { 1 } { 3 } } \right)$

Correct Answer:

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