Consider the Following Problem

Essay

Consider the following problem.Maximize Z = 3x₁ + 4x₂ + 8x₃,subject to 2x₁ + 3x₂ + 5x₃ ≤ 9 x₁ + 2x₂ + 3x₃ ≤ 5 and x₁ ≥ 0,x₂ ≥ 0,x₃ ≥ 0.Let x₄ and x₅ denote the slack variables for the respective functional constraints.After we apply the simplex method,the final simplex tableau is While doing postoptimality analysis,you learn that some of the parameter values used in the original model just given are just rough estimates,where the range of likely values in each case is within ± 50 percent of the values used here.For each of the following parameters,perform sensitivity analysis to determine whether this uncertainty might affect either the feasibility or the optimality of the above basic solution.Specifically,for each parameter,determine the allowable range of values for which the current basic solution (perhaps with new values for the basic variables)will remain both feasible and optimal.Then,for each parameter and its range of likely values,indicate which part of this range lies within the allowable range and which parts correspond to values for which the current basic solution will no longer be both feasible and optimal.(a)Parameter b₂ (b)Parameter c₂ (c)Parameter a₂₂ d)Parameter c₃ (e)Parameter a₁₂ (f)Parameter b₁