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While solving a linear programming problem by simplex method, if all ratios of the right-hand side (bi) to the coefficient, in the key row (aij) become negative, then the problem has which of the following types of solution?
- a)An unbound solution
- b)Multiple solutions
- c)A unique solution
- d)No solution
Correct answer is option 'A'. Can you explain this answer?
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While solving a linear programming problem by simplex method, if all r...
While solving a linear programming problem by simplex method, if all the ratios of the right hand side (bi) to the coefficient in the key row (aij) become negative, it means problem is having unbounded solution.
Most Upvoted Answer
While solving a linear programming problem by simplex method, if all r...
Explanation:
Simplex Method:
The simplex method is an iterative procedure used to solve linear programming problems. It starts with an initial feasible solution and then iterates to improve the objective function value until an optimal solution is reached.
Ratios of the Right-Hand Side to Coefficients:
In the simplex method, the ratios of the right-hand side (bi) to the coefficients (aij) in the key row are calculated. These ratios are used to determine the pivot column and pivot row in each iteration of the simplex method.
Types of Solutions:
There are four types of solutions that can be obtained while solving a linear programming problem by the simplex method:
a) Unbounded solution: If all the ratios of the right-hand side to the coefficients in the key row become negative, it indicates that the objective function can be improved indefinitely. This implies that the feasible region is unbounded, and there is no optimal solution to the problem.
b) Multiple solutions: If there are multiple optimal solutions to the linear programming problem, it means that there are different combinations of decision variables that can yield the same optimal objective function value.
c) Unique solution: If there is only one combination of decision variables that yields the optimal objective function value, then the problem has a unique solution.
d) No solution: If the feasible region is empty or there are no feasible solutions that satisfy all the constraints, then the problem has no solution.
Answer Explanation:
In the given problem, if all the ratios of the right-hand side to the coefficients in the key row become negative, it indicates that the objective function can be improved indefinitely. This implies that the feasible region is unbounded, and there is no optimal solution to the problem. Therefore, the correct answer is option 'A' - An unbounded solution.
Simplex Method:
The simplex method is an iterative procedure used to solve linear programming problems. It starts with an initial feasible solution and then iterates to improve the objective function value until an optimal solution is reached.
Ratios of the Right-Hand Side to Coefficients:
In the simplex method, the ratios of the right-hand side (bi) to the coefficients (aij) in the key row are calculated. These ratios are used to determine the pivot column and pivot row in each iteration of the simplex method.
Types of Solutions:
There are four types of solutions that can be obtained while solving a linear programming problem by the simplex method:
a) Unbounded solution: If all the ratios of the right-hand side to the coefficients in the key row become negative, it indicates that the objective function can be improved indefinitely. This implies that the feasible region is unbounded, and there is no optimal solution to the problem.
b) Multiple solutions: If there are multiple optimal solutions to the linear programming problem, it means that there are different combinations of decision variables that can yield the same optimal objective function value.
c) Unique solution: If there is only one combination of decision variables that yields the optimal objective function value, then the problem has a unique solution.
d) No solution: If the feasible region is empty or there are no feasible solutions that satisfy all the constraints, then the problem has no solution.
Answer Explanation:
In the given problem, if all the ratios of the right-hand side to the coefficients in the key row become negative, it indicates that the objective function can be improved indefinitely. This implies that the feasible region is unbounded, and there is no optimal solution to the problem. Therefore, the correct answer is option 'A' - An unbounded solution.
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While solving a linear programming problem by simplex method, if all ratios of the right-hand side (bi) to the coefficient, in the key row (aij) become negative, then the problem has which of the following types of solution?a)An unbound solutionb)Multiple solutions c)A unique solutiond)No solutionCorrect answer is option 'A'. Can you explain this answer?
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