Questions on Simplex algorithms and Sensitivity analysis: By using simplex algor
ID: 466136 • Letter: Q
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Questions on Simplex algorithms and Sensitivity analysis: By using simplex algorithm to solve a linear program with objective to be maximized, under which condition the problem has unique optimal solution? Assume by Simplex algorithm, we obtain the following two optimal solutions in two tableaus, how can you express all possible optimal solutions? 1^st optimal solution: x_1 = 2, x_2 = 0, x_3 = 6; and 2nd optimal solution: x_1 = 1.5. x_2 = 3.x_3 = 2.6. For a linear program with objective to be maximized, under which condition the problem is unbounded? In sensitivity analysis, assume that the coefficient of a basic variable in the objective function changes within a range that the current basis remains optimal, will the optimal solution for decision variables change? How about the optimal objective value? In sensitivity analysis, when the right-hand-side (RHS) of a constraint changes, how can you find range for this RHS in which the current basis remains optimal?Explanation / Answer
2) Linear program gets maximized Under decision variables, the values of the decision variables satisfy the set of constraints which brings satisfy of all constraints for a optimal solution it could be equality or inequality. According to that simplex algorithm considered a extreme point of integer to make LP as optimal solution. Finally Linear program would contain the limited resources condition satisfied able to solve the linear.
2.3)Linear program is unbounded if the optimal solution is un bounded under maximized, then LP has changed to transformed into an equivalent problem in standard form. Moreover unbounded caused the limited resources as unlimited it affect limited sources conditions for the LP. Unbounded variables also infinite.
2.4)The optimal value of the decision variables as well as slack were not changed because right hand value of any constraints modify the optimal value of the objective, it makes us to give the shadow price to the constraints, that constraints contains non negativity.
2.5)The values of RHS of constraints changed, it impact to change optimal solution ranges and as well as objective values also but RHS change beyond the limit it make change in slack also.
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