lean_workbook_plus_76604

Prove that for any positive numbers $a, b, c$ such that $a > b > c > 2$, the expression $\max\{2a, \frac{3}{b}\} + \max\{3a, \frac{3}{2c}\} + \max\{\frac{3c}{2}, \frac{2}{a}\}$ is greater than 10.