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 w-10

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!