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).