GATE 2021 MA – Question 42
Maximize c₁x₁+c₂x₂ under three inequalities a_i₁x₁+a_i₂x₂≤b_i (i=1,2,3),x≥0. A feasible (p,q) has c₁p+c₂q=6, and all feasible objectives lie in [−5,12]. Which is not necessarily true?
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Correct answer: (B) The feasible region is bounded.
Explanation
A nonempty polyhedron with a bounded-above linear objective has an attained finite optimum, proving A; strong duality gives D. Weak duality bounds each dual objective below by the feasible primal value 6, proving C. The region itself can still be unbounded in a direction along which the objective is constant, so **B** is not guaranteed.