Lesson eLearning

Which of the following statements about the simplex method is correct?

easy MCQ 1 mark Class 12 · Mathematics · Linear Programming
  1. The simplex method always terminates in a finite number of iterations for any linear programme.
  2. Degeneracy can cause the simplex method to cycle, but anti‑cycling rules prevent infinite loops.
  3. In each iteration the objective function value always decreases.
  4. The method can be applied directly to problems with fractional coefficients without any transformation.
Answer
Degeneracy can cause the simplex method to cycle, but anti‑cycling rules prevent infinite loops.

The correct answer is Degeneracy can cause the simplex method to cycle, but anti‑cycling rules prevent infinite loops. — Option A incorrectly claims termination for *any* LP; unbounded problems cause non‑termination. Option B correctly describes degeneracy leading to possible cycling and that anti‑cycling rules (e.g., Bland’s rule) prevent infinite loops. Option C is wrong because objective value is non‑decreasing for maximisation problems. Option D is incorrect; fractional coefficients can be handled but may require scaling. Thus option B is the correct statement.

Step-by-step solution

  1. Recall the theoretical property: the simplex method visits basic feasible solutions and each visit improves or maintains the objective. For bounded problems it must reach optimality in finite steps unless cycling occurs.
  2. Option A incorrectly claims termination for *any* LP; unbounded problems cause non‑termination. Option B correctly describes degeneracy leading to possible cycling and that anti‑cycling rules (e.g., Bland’s rule) prevent infinite loops. Option C is wrong because objective value is non‑decreasing for maximisation problems. Option D is incorrect; fractional coefficients can be handled but may require scaling. Thus option B is the correct statement.
Common mistake: Thinking that the simplex always terminates without cycling issues

Concept tested: Correct properties of simplex

Published · How this solution was prepared and checked

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