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In an LPP if one of the decision variable is zero then the solution is
- a)unique optimal
- b)infeasible
- c)degenerate if the redundant constraint is fully consumed
- d)unbounded
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In an LPP if one of the decision variable is zero then the solution i...
Explanation:
There are certain implications when one of the decision variables in a Linear Programming Problem (LPP) is zero. Let's break down the answer in detail:
Degenerate Solution:
When a decision variable is zero in an LPP, it may lead to a degenerate solution. A degenerate solution occurs when the redundant constraint is fully consumed, meaning that the constraint involving the zero decision variable no longer plays a role in determining the feasible region. This can result in the degeneracy of the solution.
Redundant Constraint:
The redundant constraint is the one that does not affect the feasible region when removed. When a decision variable is zero, it implies that the corresponding constraint is fully utilized and no longer contributes to defining the feasible region. This can lead to degeneracy in the solution.
Characteristics of Degenerate Solutions:
Degenerate solutions can complicate the optimization process as they may require additional iterations to reach the optimal solution. They can also affect the efficiency of the algorithm used to solve the LPP. Therefore, it is essential to be aware of the presence of degenerate solutions in order to address them effectively.
In conclusion, when a decision variable is zero in an LPP, it can lead to a degenerate solution if the redundant constraint is fully consumed. Understanding the implications of degeneracy is crucial in optimizing the solution to linear programming problems.
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In an LPP if one of the decision variable is zero then the solution isa) unique optimalb) infeasiblec) degenerate if the redundant constraint is fully consumedd) unboundedCorrect answer is option 'C'. Can you explain this answer?
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