QUESTION $3$

If $x,y,z$ are three positive numbers whose sum is $5$ and such that the quantity $x{y}^{2}z$ is minimum, then $xyz=$

a$.\frac{9}{16}$

b$.\frac{1}{16}$

c$.\frac{27}{32}$

d$.\frac{25}{32}$

e$.\frac{125}{32}$