How do you find the boundaries of a volume defined by
Various ways. Projection is one such way.
Simply eliminate all the 'z's and see wht it looks like from the point of view of the x-y plane.
Do the same for x-z and y-z.
Are you sure you must use dxdydz? Often there is one way that is easier than another. Maybe dydzdx would be more straight-forward. You must keep your eyes open.
Exploit symmetries and redundancies. I don't see much in this one except that the first and third constraints are a little odd. If z > 0, does the third one mean anything? Subtract 3z in the first and compare it to the third. What does that mean?