Washer and Laundry Sink Drain

[M4Gallagher]

I am adding new laundry room (remodel). I have gone through and read as many posts on the forum as possible with similar question. Can someone verify this would be the correct design for Washer drain and laundry sink draining into common 2" inch drain with 1.5" vent? I am in Michigan and will be doing work myself. Couple of other questions, can a double Wye be used connecting both sink and washer to vertical drain? Or if not, would I use single Wye for each? Is the washer vent tie in (green) needed? The 2 inch vertical drains below floor into 3.5" horizontal drain.

Thank You.

Bret