Question 87
Determine the maximum possible value of the expression
$$
27 a b c + a \sqrt{a^{2} + 2 b c} + b \sqrt{b^{2} + 2 c a} + c \sqrt{c^{2} + 2 a b}
$$
where $a, b, c$ are positive real numbers such that $a + b + c = \frac{1}{\sqrt{3}}$.
$$
27 a b c + a \sqrt{a^{2} + 2 b c} + b \sqrt{b^{2} + 2 c a} + c \sqrt{c^{2} + 2 a b}
$$
where $a, b, c$ are positive real numbers such that $a + b + c = \frac{1}{\sqrt{3}}$.