The Graphical Method is used to solve a linear programming problem (LPP) with two variables by plotting constraints on a graph and finding the optimal solution visually.

약쩹 Steps in Graphical Method

1. Formulate the LPP

Identify:

• Decision variables (e.g., $x,y$)
• Objective function (maximize/minimize $Z$)
• Constraints

2. Convert Inequalities into Equations

Change each inequality into an equation to draw lines.

Example:

$$x+yྤ4༒x+y=4$$

3. Plot the Constraint Lines

Draw each equation on the graph (x-axis and y-axis).

4. Identify the Feasible Region

• Shade the region that satisfies all constraints.
• This common shaded area is called the feasible region.

5. Find Corner (Vertex) Points

Determine the intersection points of the feasible region.

6. Evaluate Objective Function

Substitute each vertex into the objective function.

7. Select Optimal Solution

• Maximum value ໒ choose largest $Z$
• Minimum value ໒ choose smallest $Z$