Consider Exercise 4 of Chapter 2, Section 3 involving the farmer and his hogs, chickens, and ostriches.

(a) Find a system of inequalities characterizing the set of all perturbation vectors \(\Delta \mathbf{b}=\left(\Delta_{1}, \Delta_{2}\right)\) for \(\mathbf{b}\) such that the optimal solution does not change under the perturbation.

(b) Express the new value of the objective function in terms of \(\Delta_{1}\) and \(\Delta_{2}\).

(c) Find the range of values of the two individual perturbations such that the current solution remains feasible and optimal.