Intro to Linear Programming

This optimization technique is so cool!!

In this video we explore the idea of Linear Programming, which is an extremely powerful constrained optimization technique. It involves maximizing or minimizing a linear function with constraints a list of linear inequalities. The feasible region is all points satisfying those inequalities, and the big question is which points in the feasible region (which looks like a polygon) give the optimum values? The big idea of linear programming is that the optimal values occur at the vertices, that is where the iso-value line first touches the polygon.

0:00 Linear Programming
1:31 The Carpenter Problem
4:20 Graphing Inequalities with Maple Learn
5:45 Feasible Region
8:29 Computing the Maximum
10:36 Iso-value lines
13:15 The Big Idea

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[DrTrefor]

**TYPO** At 13:16 when I introduce the Big Idea I call the region concave when I mean convex!!!

[ikersanchez]

It would be great to have a series of this topic. You would actually help a lot of not only math students, but those who are involved with economics, accountability, tourism, engineering, actuarial and computer sciences.
Great video, Dr. Trefor!

[chibbyne]

Your enthusiasm is contagious and the way you presented the example, then the intuition and later the more formal geometric solution felt so much simpler than parsing the Wikipedia article. Thanks a lot!

[WRpauldirac]

Amazing explanation! Just to point out that at 9:54 the actual value of f(0, 10) is not equal to 1800 but to 2000, having f(x, y) = 180x + 200y. Just a simple variable confusion. Thanks for this clear introduction to LP, Dr. Trefor.

[lahirujeewantha]

up to now this is the most clear explanation about linear programming.. @3.44 It was very evident what is linear programming is.. Thank you professor

[MrRomulocunha]

you channel is absolutely amazing, just wanna say i learn so much from watching it. thx for sharing your knowledge.

[vuraxis]

As cool as simplex is in concept, carrying it out is the most mind-numbing thing I've ever had to do in maths by miles

[Enderj]

This sounds more like graphical solutions of 2-decision variable LP problems. The simplex method requires conversion of the LP to standard form among other things I'm about to learn today in class. For those watching this and reading here, the cornerpoint method he shows is super easy. Find the x/y intercepts of each corner of the region, plug those (x, y) values into the objective function and find your MIN/MAX value from that table.

Great video nonetheless! Thank you

[charlieobimbo]

7:50 Actually all of the wood and all the labor does not always give one
the optimal solution. This depends on the slope of the optimization function. Thus one needs to check all the corner points, except for the origin.

In this case the corner points are: (0, 10); (40/3, 10/3); (16, 0)

If the Optimization function is:

a) 2y + 3x then the optimal point is (16, 0)
b) 3y + x then the optimal point is (0, 10)

Professor Charlie Obimbo

[michaljaros]

Great explanation, you saved my studies today. Please, keep making videos

[much-love-]

Great explanation, and I can see you're passionate about this / about math, which is awesome!! Keep doing what you love and teaching with passion

[tuongnguyen]

I hope professor Trefor Bazett could cover Convex Optimization in the future. Study with him is really energetic and engaging

[dariuszspiewak]

A convex shape is one where each two points belonging to the shape can be connected with a straight line fully contained in the shape.

[KatlegoMmadi]

Coming from an economics background this makes so much sense. I now know the math behind the concept of equilibrium 😄

[ningxinzheng]

Thank you Dr. Trefor, I was so confused in the lecture, your video is so nice and clear!

[ronhernandez]

this is amazingly simple in comparison to what i was looking for which is the actual simplex algorithm

[christianevans]

Any suggestions on where to find more videos on Linear Programming and the Simplex Method?

I attend Valdosta State University in Georgia. We have a course dedicated to going beyond this topic which is called Operations Research. The professor is encouraging of Data Science. We've covered this, slack variables, Tableau method, Anti-cycling rule, 2-Phase Simplex Algorithm for the 1st exam. Later we go on to learn MATLAB & R language.

[dilipbarman]

What a cool video! I'm introducing linear programming to my algebra students in 2 days and including a link to your nice video. I'm glad that I found your resources!

[reubensolomon]

U're the best. U just save me hours of head breaking maths

[yeetonykp]

I took a linear programming in uni years ago. I get a pass then that's it.
Now watching your video I truly know what it is about. Thanks.