Can a basic variable be the entering variable in Simplex method?

Question

I have got from my teacher that "the entering variable in a maximization problem is the non-basic variable having the most negative coefficient in the Z- row"

I think X1,X2 are non basic and Z,S1,S2... are basic. And I think non of S's can be chosen as entering variable.

But by seeing this

(http://college.cengage.com/mathematics/larson/elementary_linear/4e/shared/downloads/c09s3.pdf) I got confused. Please help me to get rid of this confusion.

thanks.

Answer 1

The entering variable can be any of the variables which have negative value in the Z-row. Basic variables have zeros in the Z-row, so they can not enter in that step.