[Help-glpk] help to formulate problem in terms of LP

[Dima Ry]

I currently deal with parallelepipeds. The task is to know is one
parallelepiped itersects other one. The geometry shown at picture :
http://www.nabble.com/file/p16782979/lp_question.gif 

I need to know is the red area of parallelepiped "a" exists or not. The red
area can be found as intersection of "a" internal area and "b" external
area. If intersection exists then "a" intersects "b"

If where a way to solve this task using LP?


There is  no problem to express internal area in terms of LP. But i wonder
if external area of "b" can be expressed?

I tried following :
for "a" following constraints :
x >= 1
x <= 3
y >= 2
y <= 3

for "b" 
x <= 2
x >= 4
y <= 1
y >= 4

Since all equation are connected with "and" operator thus "x <= 2 and x >=
4" will issue "no solution"

Thanks in advance for any ideas.
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