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Simplex made Simple

Audience:

Linear Programming is one of the most useful mathematical tools whose application ranges from engineering, operations and research to business management. Hence, there is a considerable literature devoted to the topic. Here, we particularly explain the Simplex Algorithm, which is one of the prominent algorithms for solving the Linear Programming Problem. Simplex Algorithm, being purely procedural, also has a beautiful geometric flavor to it. However, in our high school and undergraduate exposition, we are usually introduced to the topic in an unintuitive tabular manner. In this interactive blog, we try to explain the geometric interpretation of it, which we believe will introduce you to a different viewpoint for looking at it. We have used the usual textbook example to keep the exposition simple. And we request that anyone use the PC Web browser, as the graphing has some responsiveness issues. (We are planning to incorporate that soon.) Assumed pre-requisite: We assume the reader is introduced to the notion of Linear Programming via the usual plotting method and the Simplex Algorithm in tabular form. This exposition is mainly to give the geometric perspective of the tabular algorithm, which we have studied. It’s our first attempt to make mathematics interactive and fun. We value your critical feedback. Thank you.

https://simplexexplain.netlify.app/

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5.03 Overall score*

52 Rank

8 Votes

3 Comments

Comments

5.3

Very practical example. It’s funny, because business classes usually shy away from the math behind optimizations like this and mathematicians usually don’t talk about the use cases for math in business. It’s nice to have the reminder. This is a good showcase, but some of your interactive graphs had me a little confused. I understand wanting to show variable isolation, but starting with a freely moving point within the valid region to then reduce down to only moving on each axis felt out of order to me. Maybe that feeling is just unique to me, however. The conclusion felt unsatisfactory, as I don’t think you really nailed-home the final answer: how much of each unit should you make? It’s not to say the answer isn’t found in the text; I was just hoping it would be made very obvious by the end. I can tell a lot of work was put into this entry, but I think that it needed one more pass of editing by an outside observer to feel out the pacing.

I liked it! I think it could use a clearer explanation of where the three linear functions come from. It’s not too difficult to figure it out, but making it extra obvious would really help beginners. Also, the green background might not be the best choice visually. Overall though, solid work … I’d give it a 7

4.5

This was a nice description of the simplex method, but it is not really clear how one variable is chosen over another when iterating over increasing the variables. Also the analogy of slack variables corresponding to a form of credits is not really working for me, because the goal is to reduce the value of the slack variables as much as possible but one wants to utilize the given credits as much as possible. So I understood first that we want the slack variables to have the highest value. I have to admit that I am a non-native English speaker, so I might have also misinterpreted something here.