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

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Sections

  • 7

    Linear Programming

    Linear programming is a mathematical optimization technique used to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships.

    Learning Practice

  • 7.1

    Introduction To Linear Programming

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

    Learning Practice

  • 7.2

    Formulating The Linear Program

    This section introduces linear programming as a framework for optimization under constraints, illustrated through a sweets shop production example.

    Learning Practice

  • 7.3

    Graphical Representation

    This section introduces linear programming as a method for optimization under constraints, using graphical representation to explore feasible regions and determine optimal solutions.

    Learning Practice

  • 7.4

    Feasible Region And Optimizing Profit

    This section introduces linear programming, focusing on feasible regions and how to optimize profit using constraints.

    Learning Practice

  • 7.5

    Simplex Algorithm Overview

    The simplex algorithm is a method for solving linear programming problems, optimizing a function given certain constraints.

    Learning Practice

  • 7.6

    Potential Issues In Linear Programming

    This section discusses potential issues related to linear programming, including constraints and the existence of solutions.

    Learning Practice

  • 7.7

    Extension Of The Example: Adding Almond Rasmalai

    This section introduces an extension to a previously discussed linear programming problem by adding a new product, almond rasmalai, altering the production constraints and objective function.

    Learning Practice

  • 7.8

    Three-Dimensional Geometrical Representation

    This section introduces three-dimensional geometrical representation in the context of linear programming and optimization problems.

    Learning Practice

  • 7.9

    Justifying Optimum Profit

    This section discusses the principles of linear programming, focusing on maximizing profit within given constraints through optimization methods.

    Learning Practice

  • 7.10

    Dual Problem In Linear Programming

    This section covers the dual problem in linear programming, explaining how constraints can be combined to derive optimizations and solutions.

    Learning Practice

References

ch50.pdf

Class Notes

Memorization

What we have learnt

  • Linear programming is used ...
  • The optimal solution for a ...
  • Complex real-world problems...

Final Test

Revision Tests