📐 Intro to Linear Programming

library(blogdown)
library(gMOIP)
# See: https://relund.github.io/gMOIP/index.html
library(knitr)
library(rgl)
rgl::setupKnitr()
options(rgl.useNULL=TRUE)
opts_chunk$set(
  echo = FALSE,
  collapse = TRUE,
  #cache = TRUE, autodep = TRUE, 
  comment = "#>",
  fig.show = "asis", 
  warning=FALSE, message=FALSE, include = TRUE, 
  out.width = "99%", fig.width = 8, fig.align = "center", fig.asp = 0.62
)

Introduction

What is Linear Programming?

Demonstration of Level Curve

Linear Programming Solver

Linear Programming in 3D view

Linear Programming Interactive

Let us say we have a Linear Programming problem with 3 variables: We define the model:

\[ Maximise : 20x_1 + 10x_2 + 15x_3\\ Subject \ to \\ \\ x_1 + x_2 + x_3 <= 10\\ 3x_1 + x_3 <= 24 \]

Here is the interactive LP Polytope:

References

1. Virginia Postrel, Operations Everything, Boston Globe, Hune 27, 2004. http://archive.boston.com/news/globe/ideas/articles/2004/06/27/operation_everything?pg=full