Maximize the objective function P = 4x + 3y subject to the constraints x ≤ 5, x + y ≤ 6, y ≤ 4, x ≥ 0, y ≥ 0.

1. $x \le 5$
2. $x + y \le 6$
3. $y \le 4$
4. $x \ge 0$ (implied for typical linear programming problems)
5. $y \ge 0$ (implied for typical linear programming problems)

The feasible region is bounded by the lines $x=0, y=0, x=5, y=4, x+y=6$.
The vertices are the intersection points of these boundary lines that satisfy all constraints: