Q.Solve each of the following L.P.P. : Maximize $z = 2x + 3y$ subject to $x - y \ge 3,\ x \ge 0,\ y \ge 0$

The feasible region of an L.P.P. is bounded if it fits entirely within some large enough circle (equivalently, some large enough square) — this typically happens when every constraint is a $\le$ upper bound combined with the non-negativity lower bounds $x\ge0,y\ge0$, closing the region off on every side. The feasible region is unbounded if it extends indefinitely in at least one direction — this typically happens when one or more constraints are only $\ge$ lower bounds with no matching upper cap on the same variables. Whether the region is bounded matters directly for whether an optimum exists: MINIMIZING a linear objective over a region that is bounded below (even if unbounded above) always has a finite minimum at a vertex, because the objective cannot keep decreasing forever once every variable is bounded below by zero and by the constraints. But MAXIMIZING a linear objective over a region that is unbounded in the direction the objective increases has NO finite maximum — the objective value can be pushed arbitrarily high by moving further and further out al …