Design & Analysis of Algorithms - Vol 3 | 7. Linear Programming by Abraham | Learn Smarter
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7. Linear Programming

7. Linear Programming

Linear programming is a mathematical optimization technique that deals with maximizing or minimizing a linear function subject to linear constraints. The chapter covers the formulation of linear programming problems through practical examples, particularly in the context of maximizing profit from product sales with various constraints. It also explains the geometric interpretation of feasible regions and solutions through vertices.

11 sections

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Sections

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  1. 7
    Linear Programming

    Linear programming is a mathematical optimization technique used to achieve...

  2. 7.1
    Introduction To Linear Programming

    This section introduces the concept of linear programming as a method for...

  3. 7.2
    Formulating The Linear Program

    This section introduces linear programming as a framework for optimization...

  4. 7.3
    Graphical Representation

    This section introduces linear programming as a method for optimization...

  5. 7.4
    Feasible Region And Optimizing Profit

    This section introduces linear programming, focusing on feasible regions and...

  6. 7.5
    Simplex Algorithm Overview

    The simplex algorithm is a method for solving linear programming problems,...

  7. 7.6
    Potential Issues In Linear Programming

    This section discusses potential issues related to linear programming,...

  8. 7.7
    Extension Of The Example: Adding Almond Rasmalai

    This section introduces an extension to a previously discussed linear...

  9. 7.8
    Three-Dimensional Geometrical Representation

    This section introduces three-dimensional geometrical representation in the...

  10. 7.9
    Justifying Optimum Profit

    This section discusses the principles of linear programming, focusing on...

  11. 7.10
    Dual Problem In Linear Programming

    This section covers the dual problem in linear programming, explaining how...

What we have learnt

  • Linear programming is used to optimize a linear objective function subject to linear constraints.
  • The optimal solution for a linear programming problem lies at one of the vertices of the feasible region.
  • Complex real-world problems can be formulated into linear programming problems to find optimal solutions.

Key Concepts

-- Linear Programming
A mathematical method for determining a way to achieve the best outcome in a given mathematical model, usually involving maximizing or minimizing a linear function.
-- Feasible Region
The set of all possible points that satisfy the problem's constraints, graphically represented in optimization problems.
-- Simplex Algorithm
An algorithm for solving linear programming problems by iterating through the vertices of the feasible region to find optimal solutions.
-- Vertices
Points in the feasible region where constraints intersect, which are candidates for the optimal solution.

Additional Learning Materials

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