Consider the following statements : (a) Revised simplex method requires lesser…
2016
Consider the following statements :
(a) Revised simplex method requires lesser computations than the simplex method.
(b) Revised simplex method automatically generates the inverse of the current basis matrix.
(c) Less number of entries are needed in each table of revised simplex method than usual simplex method. Which of these statements are correct ?
- A.
(a) and (b) only
- B.
(a) and (c) only
- C.
(b) and (c) only
- D.
(a), (b) and (c)
Attempted by 7 students.
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Correct answer: D
Answer: All three statements (a), (b) and (c) are correct.
Reasoning:
Statement (a): The revised simplex method typically requires fewer computations per iteration than the full tableau simplex because it operates on the basis and computes products with the basis inverse (or its factorization) rather than performing row operations on the entire tableau. This is especially true for large, sparse problems.
Statement (b): The revised simplex maintains and updates a representation of the basis inverse (or more commonly its factorization, e.g. LU or using eta updates). That means the effect of the current basis inverse is available across iterations without recomputing it from scratch, so the statement that the inverse is generated/maintained is effectively correct.
Statement (c): The revised simplex stores only the basis columns and a few auxiliary vectors (such as the basis inverse acting on certain vectors) instead of the full tableau, so the number of stored entries per iteration is much smaller than in the usual simplex tableau.
Because each statement is supported by the points above, all three statements are correct.