How many fixtures can 2" drain handle?

I am remodeling the kitchen area. I want to combine two 1.5" drains (one going to the kitchen and one to the bath lav) and run one 2" drain horizontally to the main stack, which is 3". Will a 2" line be able to handle both of these ok?

drain

Yes, as long as distance and venting issues, if a factor, are addressed properly.