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Crack the Code of Optimization: the Simplex Method for Students and Analysts
- Operational research emerged during World War II combining Mathematics, Statistics, Economics, Logistics, and Engineering.
- The goal was to apply scientific methods to military decision making and optimization problems.
- In 1947, George B. Dantzig formalized the general linear programming problem.
- Linear programming is used in various fields like distribution, airline scheduling, meal planning, and capital allocation.
- Constraints, like labor and machinery limits, are integral to the linear programming model.
- Coefficients in the objective function represent marginal profits.
- Non-negative restrictions ensure quantities cannot be negative.
- Optimization involves maximizing profit or efficiency.
- The Simplex Method involves iterating to improve solutions by pivoting.
- Pivot columns are chosen based on negative elements in the objective row.
- Pivot rows are determined based on ratios of constants to pivot columns.
- Pivot elements are used to form unit vectors in the tableau.
- Further iterations are made until no negative elements exist in the objective row.
- The final solution provides optimal production levels maximizing profit.
- The process involves converting pivot columns to unit vectors for maximizing efficiency.
- The Simplex Method enables efficient optimization by iteratively improving solutions.
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