一、Fill in the Blanks (8 points per question, total 64 points)
1. If positive numbers $a$, $b$, $c$ satisfy $a+2b+3c=abc$, then the minimum value of $abc$ is $\qquad$.
$-1.9 \sqrt{2}$.
From $a b c=a+2 b+3 c \geqslant 3 \sqrt[3]{6 a b c}$ $\Rightarrow a b c \geqslant 9 \sqrt{2}$.
When $a=3 \sqrt{2}, b=\frac{3 \sqrt{2}}{2}, c=\sqrt{2}$, $a b c$ achieves the minimum value $9 \sqrt{2}$.