This problem refers to Example 3 of Chapter 2, Section 3, which is repeated below.

(a) Find the set of perturbations of the form \((\Delta, \Delta, \Delta)\) to the column of \(x_{1}\) constraint coefficients that do not change the optimal solution.

(b) If \(\Delta=-2\), find the resulting perturbed final tableau, and use it as the initial tableau in the simplex method to find an optimal solution for the perturbed problem. (Hint: Use Exercise 5.)

maximize: f = x1 + 3x2 X1 + 2x2 3 2x1 + X2 3 subject to: X1 + X2 2 X1, X2 IV 0