Inconsistent teachings on how to choose a non basic variable to enter the basis (primal simplex)

During the primal simplex algorithm, a non-basic variable must be chosen to enter the basis.

Many resources on the subject choose a variable based solely on its coefficient in the row of the tableau corresponding to the objective, whereas others calculate reduced costs before making a choice.

Why is there not consistency, and is one more popular in practice?

• The coefficient of $x$ in the objective row of a simplex tableau is the reduced cost of $x.$
– prubin
Commented Sep 20, 2022 at 3:30
• Is there multiple definitions for reduced cost? In this video, they calculate c_j - z_j where z_j is the dot product of c_B and the j-th column of the tableau. In this video they just choose based on the coefficient alone.
– Ram
Commented Sep 20, 2022 at 3:51
• Maybe the c_B and the coefficients of the basis variables in the objective row are two different things?
– Ram
Commented Sep 20, 2022 at 3:54
• I think I see where I went wrong. Thanks @prubin
– Ram
Commented Sep 20, 2022 at 4:21

• Welcome back! ${}$ Commented Sep 20, 2022 at 12:24