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Optimization - Linear Programming

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Bounded Variable in LP

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Solution within a specific range for variables.

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Linear Programming in Diet Problems

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Optimal solution representing the most cost-effective diet satisfying all nutrient requirements.

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Linear Programming in Transportation

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Optimal solution for the transportation of goods to minimize cost.

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LP for Cutting Stock Problems

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Optimal solution that minimizes waste material when cutting raw materials into pieces.

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Shadow Price

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Value representing the rate of improvement in the objective function per unit increase in the right-hand side of a constraint.

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Linear Programming in Finance

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Optimal solution for investment portfolio to minimize risk or maximize return.

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LP for Network Flow Problems

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Optimal solution for flow distribution to minimize transportation cost over a network.

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LP for Airline Crew Scheduling

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Optimal solution to determine the most efficient crew assignments.

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LP for Energy Management

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Optimal energy production and distribution to minimize costs or environmental impact.

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Unbounded Linear Programming Problem

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The objective function can increase indefinitely.

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Sensitivity Analysis

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Examines how the optimal solution changes with variations of input parameters.

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Linear Programming for Blending Problems

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Optimal solution for mixing ingredients to achieve a desired blend at minimal cost.

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Linear Programming in Manufacturing

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Maximize profit or minimize costs based on production constraints.

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LP for Project Management

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Optimal allocation of resources to tasks in a project.

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Simplex Method Basics

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Optimal solution found at a vertex of the feasible region.

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Feasible Solutions Space

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Optimal solution where the objective function has its most extreme value.

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Linear Programming for Staff Scheduling

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Optimal solution that ensures adequate staffing while minimizing cost.

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LP for Production Scheduling

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Optimal scheduling of production runs to meet demands in a timely manner.

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Dual Linear Programming Problems

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Every LP problem has a corresponding dual problem with an optimal solution that gives the same objective value.

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LP for Facility Location

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Optimal solution where to build facilities to minimize operational and transportation costs.

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LP for Crop Planning

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Optimal solution for what crops to plant to maximize profits or meet production goals.

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Degeneracy in Linear Programming

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Occurs when a pivot operation does not result in a change in the objective function value.

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Integer Linear Programming

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Optimal solution must be integer values.

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Infeasible Linear Programming Problem

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No solution exists that satisfies all the constraints simultaneously.

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Reduced Cost in Simplex

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Zero for basic variables at optimality, and non-positive for maximization or non-negative for minimization for non-basic variables.

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