Q.Find feasible solution for each of the following system of linear inequations graphically : $3x + 4y \ge 12,\ 4x + 7y \le 28,\ x \ge 0,\ y \ge 0$

A solution of an L.P.P. is any set of values of the decision variables. A feasible solution is a solution that satisfies ALL of the given constraints (including non-negativity) simultaneously — it is a point that could actually be carried out in the real situation the problem describes. The feasible region (also written as the set $S$) is the set of ALL feasible solutions taken together — graphically, it is the region of the plane common to every constraint's half-plane, found by shading each constraint's half-plane separately and then keeping only the portion shaded by every one of them. Because each individual constraint's half-plane is convex, and the intersection of convex sets is itself convex, the feasible region of an L.P.P. is always a convex set (Theorem 1 of section 7.2.3) — usually a convex polygon when the region is bounded, but it can also be an unbounded convex region (for example, when every constraint only impo …