Week 4: The Simplex Method
Profits and pollutionThis week's question is: what can a local community do to get a steel plant to pollute less? Let's put ourselves in the community's shoes. We accept that the steel company wants to maximize profits. We have leverage on the company through taxes and levies. How should we deploy those to minimize the pollution from the plant? Hopefully you noticed the words maximize and minimize! There should be a way to model this as an optimization problem. And there is, but it has three variables. That means we will have a feasible set defined by three axes, so we can't draw it on a sheet of paper, which means we can't solve it using our graphical technique. What to do? It turns out we can represent a multidimensional linear programming model in a matrix 🤯, and find the optimal vertex by pivoting the matrix according to some well-defined rules. The rules we will follow for our pivoting are defined by the Simplex Method. It's an involved procedure, and is as long as any we will encounter in this course, so if you can manage this you've seen the worst 😅. Like last week we'll start with some simple problems to learn the technique, and then turn our attention back to the question we really care about, how to diminish pollution from the steel plant. So, we are back to pivoting matrices this week, but this time we'll have our computers do the pivoting for us using an online tool. (Excel can do this, but only through its Solver add-in which is not included in the educational edition of Office 365). The end of the beginningThis week marks the end of the first segment of the course on linear models. Next week we will turn to nonlinear models, and from there work our way through some topics from calculus that will enable us to model change and accumulation in systems. Reminder: Exercise Set 3.1 is due by 10:30 am Monday!Be sure to give or send me your work. Don't let these easy marks slip through your fingers. That's all for now!See you soon,
|
