
Linear Programming
I could use some help understanding how to work with a tableau for a Phase I linear programming problem.
Minimize 3x1 + 5x2
Subject to: 2x1 + x2 <= 6
x2 <= 3
x2>=1
3x1 + 6 x2 >= 9
I’m fairly confident I set up the surplus and slack variables correctly. For the initial Phase I canonical tableau, I get the following:
X1 x2 x3 x4 x5 x6 y1 y2 b
2 1 1 0 0 0 0 0 6
0 1 0 1 0 0 0 0 3
0 1 0 0 1 0 1 0 1
3 6 0 0 0 1 0 1 9
3 7 0 0 1 1 0 0 w10
From this point, I tend to get helplessly lost. I sorta get how I am supposed to use ratio tests to determine which variable leaves the tableau and which one enters, but I’m definitely not 100% of the way there yet in terms of understanding.
Any help or guidance will be appreciated. Thanks!