Mathematics · Linear Programming
Given that xB = (x3, x2, x1)T forms the optimal basis of a Linear Programming Problem (LPP) with basis matrix B and inverse: B-1 = [ α β -β ; 0 γ 0 ; 0 -β β ]. If (p, q, r) is the optimal solution of the dual of this LPP, and the objective function values match, which of the following expressions relates directly to the fundamental theorem of duality regarding the optimal dual variables?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1p2 + q2 + r2 = 17/4
- 2p + q + r = cBT B-1 &mathbf;1, representing the sum of dual variables as a linear combination of the inverse basis elements✓
- 3α - 3β + 4γ = 1
- 4α + 3β + 2γ = 3
Correct answer
p + q + r = cBT B-1 &mathbf;1, representing the sum of dual variables as a linear combination of the inverse basis elements
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