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Hi I have been reading about Dantzig-Wolfe decomposition from Bazaraa (Linear Programming and Network Flow).

The master problem shown below. Why is it that $(w, \alpha) = c_B B^{-1}$ where $w$, and $\alpha$ are the dual variables for equation 7.1 and 7.2 respectively?

Master problem for Dantzig-Wolfe Decomposition

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Because $c_BB^{-1}$ represents the primal objective value and by strong duality theorem, if the solution is optimal then primal objective value must be equal to dual objective value.

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