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On solving an LPP using simplex method, the optimality is reached for a maximization problem when
- a)All the elements in the objective function row are zero
- b)All the elements in the objective function row are non-negative
- c)All the elements in the objective function row are positive
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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On solving an LPP using simplex method, the optimality is reached for...
Explanation:
Objective Function in Linear Programming:
In linear programming, the objective function is a mathematical representation of the goal or outcome that needs to be optimized. In a maximization problem, the objective function is typically to maximize profit, revenue, efficiency, etc.
Optimality in Simplex Method:
The simplex method is an iterative procedure used to solve linear programming problems. It involves moving from one feasible solution to another in order to optimize the objective function. The optimality is reached when no further improvements can be made to the objective function value.
Condition for Optimality:
In the simplex method for maximization problems, optimality is reached when all the elements in the objective function row are non-negative. This is because the objective function row represents the coefficients of the variables in the current basic feasible solution. If all these coefficients are non-negative, it means that increasing any variable will only further improve the objective function value.
Therefore, when all the elements in the objective function row are non-negative, the current basic feasible solution is optimal and no further iterations are needed. This condition signifies that the optimal solution has been found and no further improvements can be made to the objective function value.
In conclusion, the optimality in a maximization problem using the simplex method is reached when all the elements in the objective function row are non-negative.
Objective Function in Linear Programming:
In linear programming, the objective function is a mathematical representation of the goal or outcome that needs to be optimized. In a maximization problem, the objective function is typically to maximize profit, revenue, efficiency, etc.
Optimality in Simplex Method:
The simplex method is an iterative procedure used to solve linear programming problems. It involves moving from one feasible solution to another in order to optimize the objective function. The optimality is reached when no further improvements can be made to the objective function value.
Condition for Optimality:
In the simplex method for maximization problems, optimality is reached when all the elements in the objective function row are non-negative. This is because the objective function row represents the coefficients of the variables in the current basic feasible solution. If all these coefficients are non-negative, it means that increasing any variable will only further improve the objective function value.
Therefore, when all the elements in the objective function row are non-negative, the current basic feasible solution is optimal and no further iterations are needed. This condition signifies that the optimal solution has been found and no further improvements can be made to the objective function value.
In conclusion, the optimality in a maximization problem using the simplex method is reached when all the elements in the objective function row are non-negative.
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On solving an LPP using simplex method, the optimality is reached for a maximization problem whena) All the elements in the objective function row are zerob) All the elements in the objective function row are non-negativec) All the elements in the objective function row are positived) None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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