Linear Programming Problems with MATLAB Implementation

Linear programming and integer programming problems are classical topics in operations research. Linear programming involves optimization using the Simplex Method, Full Simplex Method, and Revised Simplex Method, while integer programming incorporates approaches such as the Cutting Plane Method, Branch and Bound Method, and 0-1 Programming. These algorithms are widely applied in optimization problems across various domains. To facilitate better understanding and practical implementation of these algorithms, we provide corresponding MATLAB source codes. The implementations include key function descriptions such as pivot operations for simplex methods, constraint handling for cutting planes, and tree traversal for branch and bound algorithms. These codes demonstrate fundamental algorithmic components like tableau manipulation, constraint generation, and solution space exploration. By running and modifying these codes, users can gain deeper insights into optimization algorithm mechanics, including iteration processes, convergence checks, and solution validation techniques. We hope these resources prove valuable for both learning and research applications in mathematical optimization.