Hello!
I have a problem with linear inequalities systems, where there are more inequalities than variables, for example:
x-3y+2z>1
x-3y+2z<3
x>0
y>0
z>0
I need to find possible answer regions for variables x, y, z, according to Wolfram Alpha, there are 5 of them:
0<x<=1 and y>0 and 1/2(-x+3y+1)<z<1/2(-x+3 y+3)
1<x<=3 and 0<y<=(x-1)/3 and 0<z<1/2(-x+3 y+3)
1<x<=3 and y>(x-1)/3 and 1/2(-x+3 y+1)<z<1/2(-x+3 y+3)
x>3 and (x-3)/3<y<=(x-1)/3 and 0<z<1/2(-x+3 y+3)
x>3 and y>(x-1)/3 and 1/2(-x+3 y+1)<z<1/2(-x+3 y+3)
I would be glad to know, how can they be calculated. I can only obtain some of them, isolating a variable, for example, z>(1-x+3y)/2, and solving the right side, as it needs to be positive (z>0).
I have a problem with linear inequalities systems, where there are more inequalities than variables, for example:
x-3y+2z>1
x-3y+2z<3
x>0
y>0
z>0
I need to find possible answer regions for variables x, y, z, according to Wolfram Alpha, there are 5 of them:
0<x<=1 and y>0 and 1/2(-x+3y+1)<z<1/2(-x+3 y+3)
1<x<=3 and 0<y<=(x-1)/3 and 0<z<1/2(-x+3 y+3)
1<x<=3 and y>(x-1)/3 and 1/2(-x+3 y+1)<z<1/2(-x+3 y+3)
x>3 and (x-3)/3<y<=(x-1)/3 and 0<z<1/2(-x+3 y+3)
x>3 and y>(x-1)/3 and 1/2(-x+3 y+1)<z<1/2(-x+3 y+3)
I would be glad to know, how can they be calculated. I can only obtain some of them, isolating a variable, for example, z>(1-x+3y)/2, and solving the right side, as it needs to be positive (z>0).