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In the solution of a linear programming problem by Simplex method, if during iteration, all ratios of right-hand side bi to the coefficients of entering variable a are found to be negative, it implies that the problem has
- a)infinite number of solutions
- b)infeasible solution
- c)degeneracy
- d)unbound solution
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In the solution of a linear programming problem by Simplex method, if...
Explanation:
When solving a linear programming problem by the Simplex method, the algorithm requires selecting a variable to enter the basis and another variable to exit the basis. In each iteration, the entering variable is selected based on the optimality condition, which involves calculating the ratios of the right-hand side (RHS) coefficients bi to the coefficients of the entering variable a.
If all ratios are negative, it means that the objective function is unbounded in the direction of the entering variable. In other words, we can increase the value of the entering variable indefinitely while still satisfying all constraints, which leads to an unbounded solution. This situation occurs when the feasible region is not bounded, and the objective function can increase or decrease without limit.
Therefore, the correct answer is option D, unbounded solution.
Summary:
- Simplex method requires selecting an entering variable based on the optimality condition.
- If all ratios of RHS coefficients to entering variable coefficients are negative, the problem has an unbounded solution.
- An unbounded solution occurs when the feasible region is not bounded and the objective function can increase or decrease without limit.
When solving a linear programming problem by the Simplex method, the algorithm requires selecting a variable to enter the basis and another variable to exit the basis. In each iteration, the entering variable is selected based on the optimality condition, which involves calculating the ratios of the right-hand side (RHS) coefficients bi to the coefficients of the entering variable a.
If all ratios are negative, it means that the objective function is unbounded in the direction of the entering variable. In other words, we can increase the value of the entering variable indefinitely while still satisfying all constraints, which leads to an unbounded solution. This situation occurs when the feasible region is not bounded, and the objective function can increase or decrease without limit.
Therefore, the correct answer is option D, unbounded solution.
Summary:
- Simplex method requires selecting an entering variable based on the optimality condition.
- If all ratios of RHS coefficients to entering variable coefficients are negative, the problem has an unbounded solution.
- An unbounded solution occurs when the feasible region is not bounded and the objective function can increase or decrease without limit.
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In the solution of a linear programming problem by Simplex method, if during iteration, all ratios of right-hand side bi to the coefficients of entering variable a are found to be negative, it implies that the problem hasa) infinite number of solutionsb) infeasible solutionc) degeneracyd) unbound solutionCorrect answer is option 'D'. Can you explain this answer?
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