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Consider the following statements regarding linear programming
1. Dual of a dual is the primal.
2. When two minimum ratios of the right hand side to the coefficient in the key column are equal, degeneracy may take place.
Select the correct answer from the codes given below
Codes:
- a)1 and 2
- b)Only 1
- c)Only 2
- d)Neither 1 nor 2 is correct
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Consider the following statements regarding linear programming1. Dual...
Explanation:
Statement 1: Dual of a dual is the primal
- This statement is true in linear programming. The dual of a primal linear programming problem results in another linear programming problem known as the dual.
- Similarly, the dual of this new dual problem will yield the original primal problem.
- Therefore, the statement "Dual of a dual is the primal" is correct.
Statement 2: When two minimum ratios of the right hand side to the coefficient in the key column are equal, degeneracy may take place
- This statement is also true in linear programming.
- Degeneracy occurs in linear programming when there are multiple minimum ratios in the key column during the simplex method.
- This situation can lead to cycling, where the simplex method keeps revisiting the same set of solutions without making progress towards the optimal solution.
- Therefore, when two minimum ratios of the right-hand side to the coefficient in the key column are equal, degeneracy may occur.
Therefore, both statements 1 and 2 are correct, and the correct answer is option 'A'.
Statement 1: Dual of a dual is the primal
- This statement is true in linear programming. The dual of a primal linear programming problem results in another linear programming problem known as the dual.
- Similarly, the dual of this new dual problem will yield the original primal problem.
- Therefore, the statement "Dual of a dual is the primal" is correct.
Statement 2: When two minimum ratios of the right hand side to the coefficient in the key column are equal, degeneracy may take place
- This statement is also true in linear programming.
- Degeneracy occurs in linear programming when there are multiple minimum ratios in the key column during the simplex method.
- This situation can lead to cycling, where the simplex method keeps revisiting the same set of solutions without making progress towards the optimal solution.
- Therefore, when two minimum ratios of the right-hand side to the coefficient in the key column are equal, degeneracy may occur.
Therefore, both statements 1 and 2 are correct, and the correct answer is option 'A'.
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