FStep 1.- Select an entering variable from among the current non-basic variables which can improve the value of the objective function.
Current non-basic variables: XE , XI,
F Objective function: z -3XE - 2XI + 0S1 + 0S2 + 0S3+ 0S4
FThus increasing the value of either of the non-basic variables will improve the current solution (z=0). Since the per-unit contribution of XE (3) is higher than XI (2) we select XE as the entering (new basic) variable.
F(Note that these per-unit contributions are the partial derivatives of the Objective Function)