jmc

$\frac{b}{a}$ will be largest if $b$ is the largest it can be, and $a$ is the smallest it can be. Since $b$ can be no larger than $1200$, $b=1200$. Since $a$ can be no less than $200$, $a=200$. $\frac{1200}{200}=6$ $6$ is $\boxed{6}$