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In summary, for simple linear programming problems with few variables, graphical visualization can be effective. However, as problems become more complex, the simplex algorithm is the preferred method due to its efficiency and ability to handle larger and more intricate linear programming models.
Simplex algorithm is generally more effective for solving complex linear programming problems
Graphical visualization is effective for solving small linear programming problems with two variables, as it provides a clear visual representation of feasible regions and optimal solutions, while the simplex algorithm is more efficient for larger problems with more variables and constraints due to its ability to handle complex scenarios systematically.
Commonly used software and tools for solving linear programming problems include Microsoft Excel's Solver add-in, MATLAB with optimization toolboxes, IBM CPLEX, Gurobi, Lingo, and AMPL. These tools help formulate and solve linear programming models, optimizing decisions in resource allocation, production planning, and more. Depending on the complexity of the problem, practitioners choose the most suitable software to find optimal solutions efficiently.