Beginner Simplex problem

Question

Good evening,

I have started studying the simplex method for some examinations I would like to take, and to be perfectly honest, I am stuck really bad. The basic examples and exercises are simple, and I can generally solve them without problem. But once I get to the actual exercise part of the book, I am given the following:

max(-x1+2x2-3x3)
x1-x2+x3+2x4=10 (1)
2x2-x3<=1 (2) => 2χ2-χ3+χ5=1
x2+2x4<=8 (3) => χ2+2χ4+χ6=8

The (1),(2),(3) are my attempts at standard form, which have not helped me. The problem I have is I cannot create the needed Identity matrix. I know that it should be x1,x5,x6, but all my calculations have come back really wrong. The rest of the exercises are of this form, and since I fail at one I fail at all. I have finished all other examination material so getting stuck here is not only a major hurdle, but a huge disappointment for me. Please, if anyone is able, give me a hint. I do not ask for a full solution. Also if someone could point me to a decent site with exercises and examples for methodologies, I would be grateful.

    Last attempt for today gives me:

B    c    b    P1    P2    P3    P4    P5    P6 
P5   0    1    0     2     -1    0     1     0
P4   0    4    0     1/2   0     1     0     1/2
P1  -1    2    1     -2    1     0     0     -1
-    z   -2    0     0     2     0     0     1  <--- All zi - cj >= 0.

Final Edit: This is indeed the answer, and the problem has infinite solutions due to due to P2=0 (which means there is another perfect efficient solution)

Answer 1

And for house-keeping reasons, the answer as edited above is:

B    c    b    P1    P2    P3    P4    P5    P6 
P5   0    1    0     2     -1    0     1     0
P4   0    4    0     1/2   0     1     0     1/2
P1  -1    2    1     -2    1     0     0     -1
-    z   -2    0     0     2     0     0     1  

The problem has infinite solutions due to due to P2=0 (which means there is another perfect efficient solution)