For Example 4 of Chapter 2, Section 3:

(a) Find the range of values of each component of a perturbation vector \(\Delta \mathbf{c}=\left(\Delta_{1}, \Delta_{2}\right)\) such that the basic solution depicted in the final tableau is still optimal.

(b) Sketch the set of all pairs \(\left(\Delta_{1}, \Delta_{2}\right)\) in the plane such that the old optimal solution is still optimal.

(c) If the profit coefficient of \(x_{2}\) in the original problem is changed to 4500, obtain the entire new "final" tableau under this perturbation. Note that it no longer represents an optimal solution. Use the simplex algorithm to obtain an optimal solution for the perturbed problem.