HMMT November 2019 E5

Let $a, b, c$ be positive real numbers such that $a \leq b \leq c \leq 2 a$ . Find the maximum possible value of

$\frac{b}{a}+\frac{c}{b}+\frac{a}{c}$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{7}{2}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.