Is it permissible and advisable to drain two bathroom lavs and a washing machine through a single 2 inch drain pipe with a run of less that 4 feet to the stack with no vent? The stack in my images also has a bathtub drain and toilet tied to it - all of this on the ground floor with no other drains or vents on this stack. I have provided two images - a photo "current" and the other image is a mock-up of my plan. I intend to move the washer drain over (laundry room is behind this wall) and add two bathroom sinks in place of a single sink.
Thanks for your help,