Find Three Positive Numbers X, Y, and Z Whose Sum $P = x y ^ { 2 } z \text { is a maximum. }$

Multiple Choice

Find three positive numbers x, y, and z whose sum is 48 and $P = x y ^ { 2 } z \text { is a maximum. }$

A) x = 10, y = 7, z = 31
B) x = 7, y = 31, z = 10
C) x = 31, y = 10, z = 7
D) x = 12, y = 24, z = 12
E) x = 12, y = 12, z = 24