We're being taught Industrial Engineering and Operations Research for the first time this semester. Referring to the book by Hamdy A. Taha, I noticed the mention of two formulae for swiftly obtaining the dual variable optimal solutions from the primal optimal tableau:
Method 1. $${\text{Optimal value of}\\dual\text{ variable }y_i}\quad=\quad{{\text{Optimal primal }z\text{-coefficient of }\\starting\text{ basic variable }x_i}\quad+\quad{Original\text{ objective}\\\text{coefficient of }x_i}}$$ Method 2. $${\text{Optimal values}\\\text{of }dual\text{ variables}}\quad=\quad{\text{Row vector of }original\\\text{objective coefficients of}\\\text{optimal }primal\text{ basic}\\\text{variables}}\quad\times\quad{\text{Optimal }primal\text{ inverse}}$$
Does anyone have an intuitive explanation from how these are derived?