Linear Programming Problems
Linear Programming Problems Concepts:
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Linear Programming (LP): A mathematical method to optimize a linear objective subject to linear inequality constraints.
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Feasible Region: The set of points satisfying the constraints in an LP problem.
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Objective Function: The function being optimized in an LP problem.
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Optimal Solution: The point in the feasible region maximizing (or minimizing) the objective function.
Important Theorems:
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Fundamental Theorem of Linear Programming: Every feasible LP problem has an optimal solution.
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Duality Theorem: Every LP problem has a dual LP problem with equivalent optimal values.
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Simplex Method: An iterative algorithm for solving LP problems by moving between feasible region vertices until reaching the optimal solution.
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Revised Simplex Method: Improvement over the Simplex method for handling variable changes in constraints efficiently.
