This problem appeared while working on a neural networks practical. There are given 12 inequalities (x_0, x_1, x_2, x_3, x_4 unknown) of the form: [tex]x_0 + ax_1 + bx_2 + cx_3 + dx_4 >= 0[/tex] or, [tex]x_0 + ax_1 + bx_2 + cx_3 + dx_4 < 0[/tex], and that there exists a set of solutions that satisfy all 12 inequalities. I have to find one of those solutions but I don't know where I can start to attack this problem? I'm unable to apply trial and error, due to the high number of unknowns. I'm not finding a rigorous methodology either. Does anyone have any suggestion? Does any software package exist that aids me to do this? Thanks a lot!