Intro to Operations Research
Spring 2016

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Lesson 2: Basic Linear Programming Modeling

In this video, I take a written description of a simple model and show how you translate it to a linear programming model. You can access the written description here.

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Lesson 3: Linear Programming Graphing and Visualization

For this lesson, I provide a couple of supplemental resources. First, if you need a refresher on graphing linear equations, view this video. Additionally, if you need help with finding the intersection of two lines (or solving a system of linear equations), I point you to this video. Lastly, the video posted below is a video I previously made that walks through an example of modeling a linear program, graphing the visualization of the linear program, and evaluating the extreme (corner) points. I start with a word problem and formulate it as a linear program (LP) using equations. I then graph the problem, and show a way of finding the optimal solution.

Details:
Word Problem to LP: Start at beginning
LP to Graph: Start at about 5:23
Graph to Optimal Solution: Start at 8:40

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Lesson 7: Linear Algebra

For this lesson, we review pertinent linear algebra definitions and concepts. For a refresher on Gaussian elimination, please view this video. Additionally, we can use Gauss-Jordan elimination to solve systems of linear equations that have an infinite number of solutions. We do this by identifying m (number of constraints) basic variables and (n-m) non-basic variables. Please view this video. Please note that towards the end of the video, the author discusses representing the solution in terms of t or another variable. We instead identify basic and non-basic variables and set non-basic variables to 0, which allows us to calculate a full numeric solution.

Lesson 11: AMPL Tutorial

Please access videos walking you through AMPL, the software we will use to solve math programs here.