The rate constants 
and 
are much larger than 
. The
intermediate B should therefore be removed rapidly, which means that the
steady-state approximation should be appropriate. You should be able to
work out the following equation using the steady-state approximation:
This means that, shortly after the establishment of the steady state, we
should have 
. The initial
rate would be 
.
This rate is roughly equal to
. This means that 
.
We want no more than 1% of the A (0.004mol/L) to be converted to
product. This means that 
so
that 
(in round numbers).