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

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

The correct answer is B. Degeneracy can cause the simplex method to cycle, but anti‑cycling rules prevent infinite loops. — Select the statement that is correct.

Step-by-step solution

  1. Read each option carefully and recall the properties of the simplex method.
  2. Option A is false because the method may not terminate for degenerate cases without anti‑cycling rules.
  3. Option B is true: degeneracy may lead to cycling, but techniques such as Bland's rule guarantee termination.
  4. Option C is false for a maximisation problem; the objective value increases (or stays same) in each iteration.
  5. Option D is misleading; while fractional coefficients are allowed, the method still requires the problem to be in standard form.
  6. Select the statement that is correct.
Common mistake: Choosing option C because of confusion between max and min

Concept tested: Properties of simplex method

Published · How this solution was prepared and checked

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