GATE ME 2026 Set 1 — Question 46
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Industrial Engineering → Operations Research → Duality & Sensitivity
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Question
An objective function of primal variables ( and ) is described below:
Minimize
subject to
is the objective function of the dual of .
, and represent the corresponding dual variables.
Which one of the following options represents the correct form of ?
Minimize
subject to
is the objective function of the dual of .
, and represent the corresponding dual variables.
Which one of the following options represents the correct form of ?
Correct answer
(A) Maximize W = 0.4 k₁ + 0.6 k₂ + 2.0 k₃ + 1.8 k₄ subject to 0.1 k₁ + 0.1 k₃ + 0.2 k₄ ≤ 0.07 0.1 k₂ + 0.2 k₃ + 0.1 k₄ ≤ 0.05 k₁, k₂, k₃, k₄ ≥ 0
Solution
The primal problem is:
Minimize subject to .
The corresponding dual problem is:
Maximize subject to .From the primal:
, , Dual objective function:
Dual constraints ():
1)
2)
This matches option (A).
Minimize subject to .
The corresponding dual problem is:
Maximize subject to .From the primal:
, , Dual objective function:
Dual constraints ():
1)
2)
This matches option (A).
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