I would like to know why here on the page 30, the author writes about absolute values, at all ?
Phase I: minimize the sum of the artificial variables, starting from the BFS wherethe absolute value of the artificial variable for each constraint, or of the slack variable in case there is no artificial variable, is equal to that of the right-handside.
He takes the aboslute values of both, left hand side and right hand side. The BFS however, may have a sign and he will then need to go back to that sign?