Discussion
Consider the following statements :
1. Sensitivity analysis provides a single value within which a parameter may change without affecting optimality.
2. While performing sensitivity analysis, the upper bound infinity on the right hand side of a constraint means that the constraint is redundant.
3. When an additional constraint is added in the LP models, the existing optimal solution can further be improved if \(z_{i} - c_{j} \ge 0\).
Which of the above are correct ?
Answer: D
The answer is All are wrong.
1 is wrong: sensitivity analysis gives a range (lower and upper limits) within which a cost coefficient or right-hand side can vary without changing the optimal basis, not a single value.
2 is wrong: an infinite upper limit on a right-hand side means the constraint has slack at the optimum (it is non-binding), so increasing its right-hand side changes nothing. That does not make it redundant: lowering the right-hand side can make it binding, and removing it can change the feasible region.
3 is wrong: adding a constraint can only shrink the feasible region, so the optimal value can stay the same or get worse, never improve. With nothing correct, D is the answer.
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