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In linear programming a basic feasible solution
- a)satisfies constraints only
- b)satisfies constraints and non-negativity restrictions
- c)satisfies non-negativity
- d)optimizes the objective function
Correct answer is option 'B'. Can you explain this answer?
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In linear programming a basic feasible solutiona)satisfies constraints...
Basic Feasible Solution in Linear Programming
Basic feasible solutions are important concepts in linear programming as they help in finding optimal solutions to optimization problems. Here's an explanation of what constitutes a basic feasible solution:
Constraints and Non-negativity Restrictions
- A basic feasible solution must satisfy all the constraints of the linear programming problem. This means that the solution must adhere to all the limitations and requirements set by the problem.
- In addition to satisfying the constraints, a basic feasible solution must also satisfy the non-negativity restrictions. This means that all decision variables in the solution must be greater than or equal to zero.
Optimizing the Objective Function
- While a basic feasible solution does not necessarily optimize the objective function, it provides a starting point for finding the optimal solution. By satisfying all constraints and non-negativity restrictions, a basic feasible solution narrows down the search space for the optimal solution.
- The optimal solution is found by further refining the basic feasible solution through techniques such as the simplex method or graphical method. These methods iteratively improve the solution until the optimal values of the decision variables are obtained.
In conclusion, a basic feasible solution in linear programming satisfies both constraints and non-negativity restrictions, setting the foundation for finding the optimal solution to the optimization problem.
Basic feasible solutions are important concepts in linear programming as they help in finding optimal solutions to optimization problems. Here's an explanation of what constitutes a basic feasible solution:
Constraints and Non-negativity Restrictions
- A basic feasible solution must satisfy all the constraints of the linear programming problem. This means that the solution must adhere to all the limitations and requirements set by the problem.
- In addition to satisfying the constraints, a basic feasible solution must also satisfy the non-negativity restrictions. This means that all decision variables in the solution must be greater than or equal to zero.
Optimizing the Objective Function
- While a basic feasible solution does not necessarily optimize the objective function, it provides a starting point for finding the optimal solution. By satisfying all constraints and non-negativity restrictions, a basic feasible solution narrows down the search space for the optimal solution.
- The optimal solution is found by further refining the basic feasible solution through techniques such as the simplex method or graphical method. These methods iteratively improve the solution until the optimal values of the decision variables are obtained.
In conclusion, a basic feasible solution in linear programming satisfies both constraints and non-negativity restrictions, setting the foundation for finding the optimal solution to the optimization problem.
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In linear programming a basic feasible solutiona)satisfies constraints onlyb)satisfies constraints and non-negativity restrictionsc)satisfies non-negativityd)optimizes the objective functionCorrect answer is option 'B'. Can you explain this answer?
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