This is a question about drain design. I plan on installing a utility bathroom. The room is about 9 feet by 4 feet. The shower will be on the left hand side, the toilet will be in the middle and the lavatory will be on the right. The soil stack is on the right about 3 feet from the lavatory. I plan on a 2″ drain line and trap for the shower which will connect to a 3″ line for the toilet via a low heel inlet 90 degree bend (3x3x2) which will then connect to the soil stock via an upturned wye (4x4x3). The lavatory will connect to the 3″ line via a 3x3x2 wye very close to the stack. In total, the shower will be about 8 feet from the stack, the toilet will be about 54″ from the stack and the lavatory will be about 3 feet from the stack. My questions are 1) is it ok to use a low heel inlet 90 degree bend this way, (2) how far from the stack can I be before I need to install a vent(s)(zone 3), (3) does the overall plan make sense? All comments will be greatly appreciated.