Minimum Floor Space Under Fixtures

I am adding a bathroom with a sink, toilet, and tub to some existing space in my attic. Currently the 2nd floor will be 18 inches from the floor below. A 3 inch drain line will have to run 30 feet horizontal and then vertical into the slab. The entire run for the 3 inch drain will consume 7 inches and leaves me with 11 inches for all the fittings. My question is what would be the minimum floor width that is need under the floor to attach all necessary traps and fittings?

The only below-floor trap would be the shower/tub.
The sink trap will be under the sink, of course, and a toilet has a built-in trap.
You need 1.4" per linear foot of slope toward the main drain (30' X .25" = 7.5").
You should have plenty of room to do what you're trying to do. Tie the tub and sink drains and vents into the toilet drain and vent.
Good Luck!
Mike