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GATE 2016 ME (ME1) – Question 65

Operations Research · Linear programming and the simplex method · 2 marks · Multiple choice

Maximize Z=15X1 + 20X2 subject to 12X1 + 4X2 ≥ 36 12X1 − 6X2 ≤ 24 X1, X2 ≥ 0 The above linear programming problem has

  1. infeasible solution
  2. unbounded solution
  3. alternative optimum solutions
  4. degenerate solution

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Correct answer: (B) unbounded solution

Explanation

Set X1=0 and choose X2≥9. Both constraints hold:4X2≥36 and−6X2≤24. Along this feasible ray, objective Z=20X2 grows without bound as X2 increases. Therefore the maximisation has an **unbounded solution, B**, rather than an unattainable feasible region.