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GATE 2023 MN – Question 19

Mineral Economics, Mine Planning, Systems Engineering · Systems Engineering · 1 mark · Multiple choice

Maximise $Z=4x_1+2x_2$ subject to $2x_1-2x_2\le20$, $4x_1\le80$, and $x_1,x_2\ge0$. Classify the solution.

  1. Unbounded solution
  2. Infeasible solution
  3. Multiple optimal solutions
  4. Unique optimal solution

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Show answer and explanation

Correct answer: (A) Unbounded solution

Explanation

Set x₁ = 0 and let x₂ grow without bound. Both inequalities remain satisfied, while Z = 2x₂ grows without bound. Thus the feasible set exists but there is no finite maximum, A. The upper bound on x₁ does not bound the positively weighted x₂.

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