I have an inequalities sytem like the following:
> x+y+z <= A > x+y <= B > x+z > C > y+z > D > x >= E
Let A,B,C,D,E be any constant value.
Notice that the coeficient of the variables are always 1. So an equation matrix will always look like this:
(1 1 1 | <= A) (1 1 0 | <= B) (1 0 1 | < C) (0 1 1 | > D) (1 0 0 | >= E)
Each row represents a plane in 3D space.
The solution to this sytem has a geometrical 3D representation which is a volumne space. So if the volume is greater than 0, there is a solution!
Is there a way to tell if all this equations have at least one feasible solution? or in other words, is there a "volume" contoured by this planes??