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If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that
- a)Right hand side of the primal constraint can be altered without affecting the optimum solution
- b)Changing the right hand side of the primal constraint will disturb the optimum solution
- c)The objective function is unbounded
- d)The problem is degenerate
Correct answer is option 'C'. Can you explain this answer?
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If at the optimum in a linear programming problem, a dual variable cor...
Explanation:
The given statement is related to the duality theory of linear programming. Duality theory provides a unique relationship between the primal and dual problems of linear programming. In the dual problem, the objective is to minimize the cost of resources required to satisfy the constraints of the primal problem.
The dual variables in the dual problem represent the cost of the resources required to satisfy the corresponding primal constraints. The values of these dual variables are used to calculate the objective function value of the dual problem.
If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that the corresponding primal constraint is binding. In other words, the primal problem is such that the optimal solution lies on the boundary of the feasible region, and any change to the right-hand side of this constraint will disturb the optimal solution.
Hence, the correct answer is option 'C', which states that changing the right-hand side of the primal constraint will disturb the optimum solution.
In summary, the zero value of a dual variable indicates that the corresponding primal constraint is binding, and any change to the right-hand side of this constraint will disturb the optimal solution. This is because the objective function is unbounded in the direction of the binding constraint.
The given statement is related to the duality theory of linear programming. Duality theory provides a unique relationship between the primal and dual problems of linear programming. In the dual problem, the objective is to minimize the cost of resources required to satisfy the constraints of the primal problem.
The dual variables in the dual problem represent the cost of the resources required to satisfy the corresponding primal constraints. The values of these dual variables are used to calculate the objective function value of the dual problem.
If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that the corresponding primal constraint is binding. In other words, the primal problem is such that the optimal solution lies on the boundary of the feasible region, and any change to the right-hand side of this constraint will disturb the optimal solution.
Hence, the correct answer is option 'C', which states that changing the right-hand side of the primal constraint will disturb the optimum solution.
In summary, the zero value of a dual variable indicates that the corresponding primal constraint is binding, and any change to the right-hand side of this constraint will disturb the optimal solution. This is because the objective function is unbounded in the direction of the binding constraint.
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If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means thata)Right hand side of the primal constraint can be altered without affecting the optimum solution b)Changing the right hand side of the primal constraint will disturb the optimum solution c)The objective function is unbounded d)The problem is degenerateCorrect answer is option 'C'. Can you explain this answer?
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If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means thata)Right hand side of the primal constraint can be altered without affecting the optimum solution b)Changing the right hand side of the primal constraint will disturb the optimum solution c)The objective function is unbounded d)The problem is degenerateCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means thata)Right hand side of the primal constraint can be altered without affecting the optimum solution b)Changing the right hand side of the primal constraint will disturb the optimum solution c)The objective function is unbounded d)The problem is degenerateCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means thata)Right hand side of the primal constraint can be altered without affecting the optimum solution b)Changing the right hand side of the primal constraint will disturb the optimum solution c)The objective function is unbounded d)The problem is degenerateCorrect answer is option 'C'. Can you explain this answer?.
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