9: Linear Programming - The Simplex Method
In this chapter, you will:
- Investigate real world applications of linear programming and related methods.
- Solve linear programming maximization problems using the simplex method.
- Solve linear programming minimization problems using the simplex method.
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- 9.2: Maximization By The Simplex Method
- The simplex method uses an approach that is very efficient. It does not compute the value of the objective function at every point; instead, it begins with a corner point of the feasibility region where all the main variables are zero and then systematically moves from corner point to corner point, while improving the value of the objective function at each stage. The process continues until the optimal solution is found.
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- 9.3: Minimization By The Simplex Method
- In this section, we will solve the standard linear programming minimization problems using the simplex method. The procedure to solve these problems involves solving an associated problem called the dual problem. The solution of the dual problem is used to find the solution of the original problem. The dual problem is a maximization problem, which we learned to solve in the last section. We first solve the dual problem by the simplex method.
Thumbnail: Polyhedron of simplex algorithm in 3D. (CC BY-SA 3.0; Sdo via Wikipedia)