# Revised Simplex Method w/o Identity Matrix

For a homework problem we're forced into using revised simplex, but I cannot seem to even get past the first step. My biggest problem is:

max z = 2x1 + 3x2 -x3
subject to:
x1 + 2x2 <= 3
2x1 + 3x2 <= 6
3x1 + 2x2 + x3 = 10


I know that this goes into:

max z = 2x1 + 3x2 -x3
subject to:
x1 + 2x2 + x4 = 3
2x1 + 3x2 + x5 = 6
3x1 + 2x2 + x3 =10


But because the last row doesn't need a slack variable (since there's an equals and adding a x6 would make this invalid), I'm left with 2 columns of a identity matrix size 3 to put as b. My foundations are a bit shaky at LP's but is it possible I can shift the constraints around? Or is there another way to do this?

• You can add an artificial variable. – callculus Apr 16 '15 at 12:52