Consider a system of linear inequalities in two variables whose solution set is called the feasible region.
a. (i) Define a feasible region in the context of linear inequalities.
b. (ii) Prove that the feasible region obtained by simultaneously satisfying any finite number of linear inequalities in two variables is always a convex set.
c. (iii) Draw a rough sketch of two intersecting half-planes to illustrate part (ii) and mark the feasible region clearly.