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A feasible solution to the linear programming problem should
- a)Satisfy the problem constraints
- b)Optimize the objective function
- c)Satisfy the problem constraints and non-negativity restrictions
- d)Satisfy the non-negativity restrictions
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A feasible solution to the linear programming problem shoulda)Satisfy ...
A feasible solution to the linear programming problem should satisfy the problem constraints.
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A feasible solution to the linear programming problem shoulda)Satisfy ...
Feasible Solution in Linear Programming
In linear programming, a feasible solution is one that satisfies all the problem constraints and non-negativity restrictions. Let's break down why option 'C' is the correct answer:
Satisfying the Problem Constraints:
- Feasibility requires that the solution must adhere to all the constraints set by the problem. These constraints define the limitations within which the solution must lie.
- If any of the constraints are violated, the solution is considered infeasible and does not provide a valid answer to the problem.
Optimizing the Objective Function:
- While satisfying the constraints is crucial, the ultimate goal in linear programming is to optimize the objective function.
- The feasible solution should not only satisfy the constraints but also maximize or minimize the objective function, depending on whether it is a maximization or minimization problem.
Satisfying Non-negativity Restrictions:
- In linear programming, variables are typically required to be non-negative, meaning they cannot take on negative values.
- The feasible solution must adhere to this non-negativity restriction to ensure the practicality and validity of the solution.
Therefore, a feasible solution in linear programming must satisfy the problem constraints, optimize the objective function, and adhere to the non-negativity restrictions. Option 'C' encompasses all these essential aspects of finding a valid and practical solution to a linear programming problem.
In linear programming, a feasible solution is one that satisfies all the problem constraints and non-negativity restrictions. Let's break down why option 'C' is the correct answer:
Satisfying the Problem Constraints:
- Feasibility requires that the solution must adhere to all the constraints set by the problem. These constraints define the limitations within which the solution must lie.
- If any of the constraints are violated, the solution is considered infeasible and does not provide a valid answer to the problem.
Optimizing the Objective Function:
- While satisfying the constraints is crucial, the ultimate goal in linear programming is to optimize the objective function.
- The feasible solution should not only satisfy the constraints but also maximize or minimize the objective function, depending on whether it is a maximization or minimization problem.
Satisfying Non-negativity Restrictions:
- In linear programming, variables are typically required to be non-negative, meaning they cannot take on negative values.
- The feasible solution must adhere to this non-negativity restriction to ensure the practicality and validity of the solution.
Therefore, a feasible solution in linear programming must satisfy the problem constraints, optimize the objective function, and adhere to the non-negativity restrictions. Option 'C' encompasses all these essential aspects of finding a valid and practical solution to a linear programming problem.
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A feasible solution to the linear programming problem shoulda)Satisfy the problem constraintsb)Optimize the objective function c)Satisfy the problem constraints and non-negativity restrictions d)Satisfy the non-negativity restrictionsCorrect answer is option 'C'. Can you explain this answer?
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