Linear Programming and Applications

This course is an introduction to linear programming and its applications. The course is divided into two parts: theoretical and practical. The theoretical part linear problems, startdard form, simplex method, revision of linear algebra and more. The practical algorithms in python to solve linear programming problems.

Linear Problems Def

The linear problem is a mathematical model that represents a situation in which the objective is to optimize a linear function subject to a set of linear constraints. The linear problem is represented by the following mathematical model:

• Objective Function:
  • Maximize: c1x1 + c2x2 + ... + cn*xn
  • Minimize: c1x1 + c2x2 + ... + cn*xn
  • c1, c2, ..., cn are the coefficients of the objective function.
• Constraints:
  • a11x1 + a12x2 + ... + a1n*xn <= b1
  • a21x1 + a22x2 + ... + a2n*xn <= b2
  • ...
  • am1x1 + am2x2 + ... + amn*xn <= bm
  • aij are the coefficients of the constraints.
• Variables:
  • x1, x2, ..., xn

Librarys and Tools

Python - Python is a programming language that lets you work quickly and integrate systems more effectively. Numpy - NumPy is the fundamental package for scientific computing with Python. Guropipy - Gurobi is the most powerful mathematical optimization solver out there. It is designed to solve large-scale mathematical optimization problems.

Getting Started

1. Ensure you have Python installed on your machine.

python --version

1. If you don't have Python installed, download it from the official website: https://www.python.org/downloads/ or if you are using a Linux distribution, you can install it using the package manager of your distribution.
2. Clone the repo.
3. You can run class projects in the folder trabalh[n] where n is the number of the project.