❖ The Simplex Method and the Dual : A Minimization Example ❖

Master the Simplex Method and Duality: Solving Minimization Problems Made Easy!

In this video, we'll explore how to use the Simplex Method and the concept of duality to solve minimization problems in linear programming. We'll take a function that we want to minimize subject to a set of constraints and show how to convert it into a maximization problem—the "dual problem"—which can then be solved using the Simplex Method. Once we find the solution to this dual problem, we'll use it to solve the original minimization problem. This notion of duality is not only fascinating but also appears in other areas of mathematics, offering insights that can prove useful in fields like geometry!

What You Will Learn:
How to convert a minimization problem into a maximization (dual) problem.
Applying the Simplex Method to solve the dual problem.
Interpreting the solution of the dual problem to solve the original minimization problem.
Understanding the concept of duality in linear programming.
Insights into how duality applies to other areas of mathematics.
📚 Check out my book: 1001 Calculus Problems for Dummies for more practice!

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#LinearProgramming #SimplexMethod #Duality #Minimization #Optimization #MathTutorial #PatrickJMT #OperationsResearch #Mathematics

[aishvetorah]

I'm gonna make a part of graduation speech about you saving student lives.

[peteshramkop.e.]

Awesome job mate. It’s been 20 years since I looked at LP since grad school... who knew it would become so relevant to everything we do today 🧐

[vishalchoure]

This was so much easier to understand here than in school. Thank you :)

[runnereatscow]

patrickJMT you saved me when I was getting my general ed math courses. Now once again, you are saving me for my Algorithms class :)

[nikkovincegonzales]

I chose Y2 as the pivot column in the initial table and got the result in the next iteration. Got lucky I guess, thanks Pat. Your method is faster than the one we were taught.

[heavencalling]

I've really understood the whole process it's much easier. The fact that I've not seated in any lectures for this semester because of lockdown and no meeting but I've understood as though I was in class and paharps much better than in class.
Thanks 🤝🤝🤝🤝🤝

[rajuacharya]

I really love your working style. Its so simple and easy to understand. Thank you for this video. Love from 🇳🇵 Nepal

[vinayaknayak]

Thanks a lot for making this video, Patrick!!Just one suggestion, if in the first step, you select the element in the second column or the second column's -8 as the pivot column, then you directly land up at the final matrix (17:50 in the video).

[nuElevenGG]

thanks! i'm sure a lot of people will find this helpful. maybe you can do a video on the geometric interpretation of the simplex method?

[rajendramisir]

Thanks Patrick. Nice review for me. I learned about the Simplex method in Finite Mathematics 28 years ago in College.

[gogvale]

I have no idea why this works, but thanks. You just saved me from my exam tomorrow ♥

[iqrandiamalik]

Loved it😊 even after 5 years, it still helped

[iDramex]

after finishing Math courses I lost hope of seeing you again until I came across this video in an operations research course.

[hencodelange]

I just caught up a week of class 2 hours before the test, thank you

[xoppa]

it would be nice to put all the simplex videos into one playlist. nice video ;p

[Graywolf]

Came looking for insight into Dual vs Primal problems for ML hw, left with a greater respect for LinAlg and an idea how row ops can be made into an algorithm. Thanks!

[mercymwanza]

😄😄I like where you say this is fun😆 it is fun when you know what you are doing, just like my lecturer always says, "have the confidence. "

[tobyto]

I read the brilliant's steps on performing this, it is trying to solve it from bottom to top, which is hard to understand.
This one explains it very clearly on how the operations go. :D

[notmimul]

I really like your energy and way of explaining it. from A-Z

[tutsyb]

You are the definition of a life saver..thank you Patrick!