jmc

Since $11<11.1<12$ we have $\lfloor 11.1\rfloor =11.$ Next we have that $2\cdot \lfloor 0.5\cdot 11.1\rfloor =2\lfloor 5.55\rfloor =2\cdot 5=10.$ Therefore, $\lfloor 11.1\rfloor +2\cdot \lfloor 0.5\cdot 11.1\rfloor =\boxed{21}.$