Boeing has begun production of the 737MAX aircraft, with the first aircraft entering the production line.  After deliveries of major components in August, production has officially begun and technicians have now joined the fuselage and wings of the first aircraft, which will be a 737-8 model.  In the photos below, the distinctive advanced winglets for the MAX are perhaps the most notable difference when compared with existing 737 models.
The MAX program is on track to have the first aircraft roll-out before year end, and begin test flights in early 2016, 
with first delivery scheduled for the third quarter of 2017 to Southwest Airlines.
Boeing will begin MAX production on a separate production line, and as the production processes are validated and proven out, they will be migrated to two additional production lines as Boeing transitions from 737NG to 737MAX production. Â The MAX family currently has 2,869 orders from 58 customers worldwide.
If the engine has to be redesigned it might delay EIS somewhat.