Graphical Method of Solving Linear Programming Problem

The graphical method is the most intuitive way to solve a linear programming problem when you have only two decision variables. Instead of diving straight into algebra, you first translate each constraint into a straight line on the $xy$-plane, then shade the region that satisfies all constraints simultaneously — this is the feasible region. The key insight is that the optimal value of the objective function (whether maximum or minimum) will always occur at one of the corner points (vertices) of this region. By evaluating the objective function at each corner, you can …