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    To graph a linear programming problem involving variables x, y, and z, follow these steps. Note that graphical methods are typically limited to two variables (x and y). For three variables, visualization requires 3D plotting or alternative methods like the Simplex algorithm.

    For Two Variables (x, y):

    1. Formulate the Problem Define the objective function (e.g., maximize or minimize Z = ax + by). List all constraints as linear inequalities (e.g., x + y ≤ 40, x ≥ 0, y ≥ 0).

    2. Plot the Constraints Convert each inequality into an equation (e.g., x + y = 40). Plot these lines on a 2D graph. Use test points to determine which side of the line satisfies the inequality. Ensure to include non-negativity constraints (x ≥ 0, y ≥ 0).

    3. Identify the Feasible Region The feasible region is the intersection of all constraint-satisfying areas. It is typically a polygon in bounded problems.

    4. Find Corner Points Calculate the coordinates of vertices of the feasible region by solving pairs of equations formed by intersecting lines.

    5. Evaluate the Objective Function Substitute each corner point into the objective function to find its value. The maximum or minimum value gives the optimal solution.

    What is graphic solution of linear programming?
    In Graphical Solution of Linear Programming, we use graphs to solve LPP. We can solve a wide variety of problems using Linear programming in different sectors, but it is generally used for problems in which we have to maximize profit, minimize cost, or minimize the use of resources.
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    Linear Programming: Graphical Method Explained ...
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  1. GeeksForGeeks
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    Graphical Solution of Linear Programming Problems

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