4. Consider the following linear programming problem. z = -531 +532 +13x3 Maximize Subject to: -11 +22 +3x3 = 20 12x1 +4x2 +1033 0. The initial and final Simplex Tableaus for solving this problem are given below. Initial Tableau: Basic Z Variable 1 81 0 82 0 21 5 -1 12 12 23 -5 -13 1 3 4 10 81 82 0 0 1 0 0 1 0 20 90 Final Tableau: Basic z Variable 1 22 0 82 0 11 0 -1 16 12 0 1 0 23 2 3 2 81 5 1 4 82 0100 0 20 1 10 a) (10 points) For what ranges of the change in the RHS of both constraints (one at a time), the current optimal basis remins optimal? b) (5 points) For what range of the change in the coefficient of xz in the objective function, the current optimal basis remins optimal? c) (10 points) Introduce a new variable x4 with C4 = 10 (the coefficient in the objective function), 414 = 3, and a 24 = 5 (the coefficients in the constraints). Find the new optimal solution of the