Solution
= Solution
Since $F_1=200+t$ and $t\ge0$, its <minimum> is attained at $t=0$:
$$
\boxed{F_1^{\min}=200,\qquad(F_2,F_3,F_4)=(0,100,50)\text{ cars per hour}.}
$$
Zero flow on the $B\to C$ arc is allowed; no strictly positive lower bound was specified.