Day 61 of 100daysofcode Challenge: Linear Programming

What is Linear Programming?

Linear programming is a method used to optimize a linear objective function, subject to a set of linear constraints. It’s a powerful tool for solving decision-making problems in various fields, such as operations research, economics, and management science.

Key Components:

Decision Variables:The variables that we want to optimize, represented by x, y, z, etc.

Objective Function:A linear function that we want to maximize or minimize, represented by f(x, y, z,…).

Constraints:A set of linear equations or inequalities that the decision variables must satisfy, represented by Ax <= b, where A is a matrix, x is the decision variable vector, and b is the right-hand side vector.

Types of Linear Programming:

Maximization Problem: Maximize the objective function, subject to the constraints.

Minimization Problem:Minimize the objective function, subject to the constraints.

How Linear Programming Works:

Formulation: Formulate the problem by defining the decision variables, objective function, and constraints.

Graphical Method: Use graphical methods to visualize the feasible region and find the optimal solution.

Simplex Method:Use the simplex method, a popular algorithm for solving linear programming problems, to find the optimal solution.

Dual Problem: Formulate the dual problem, which is used to find the optimal solution and sensitivity analysis.