Intro to Linear Programming

This optimization technique is so cool!!
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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!!!

[@SAAARC]

I was wondering what a convex region would look like and I see this comment lol

[@georginamuluki2134]

Okay....I understood, thank you

[@imranq9241]

Nice, i was just confused about that and see that now

[@chibby0ne]

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!

[@ikersanchez8222]

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!

[@lahirujeewantha5208]

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

[@ningxinzheng4382]

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

[@dilipbarman9322]

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!

[@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

[@MrRomulocunha]

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

[@DrTrefor]

Glad you enjoy it!

[@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.

[@michaljaros1380]

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

[@ronhernandez8857]

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

[@vuraxis953]

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

[@DrTrefor]

Haha that is true. But tbh when actually done in practice we're just to program it into the computer and get them to compute out the vertices.

[@vuraxis953]

@@DrTrefor yeah unfortunately A level further maths doesn't seem to appreciate that lmao. It doesn't go into stupid amounts of detail in the A level but I have had to do a two-stage simplex with 4 variables and 4 constraints in the past, which took me about 40 minutes to do the one question, it was pure suffering

[@avanishparmessur5032]

@@vuraxis953 same for some uni courses. you have to do it manually

[@vuraxis953]

@@avanishparmessur5032 yup, I'm on the MMORS scheme at Cardiff now because I wanna go into stats and they have no maths and stats course without OR, and the OR modules do unfortunately have simplex in. Not looking forward to revisiting it

[@avanishparmessur5032]

@@vuraxis953 interesting, im at cardiff too in data sci :)

[@tuongnguyen9391]

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

[@yeetonykp4569]

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.

[@dariuszspiewak5624]

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.

[@reubensolomon4162]

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

[@KatlegoMmadi]

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

[@iloveutubealotandmor]

Great explanation. Please keep up the good work

[@MossesRoss]

Just wanted to say you're a wonderful teacher

[@StokesburyUSA]

Wonderful explanation. Thank you for the video.

[@IMadeOfClay]

Brilliant video. Thank you professor!

[@DrTrefor]

Glad you liked it!

[@vinayajoseph7025]

Loved your lecture and your T-shirt

[@axisepsilon514]

Holy shit, thank you! Had to take one in my senior year anyways, might as well just preview for fun

[@Ender7j]

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

[@prashanthkumar0]

really great video on the concept

[@rakhshandamujib2793]

My teacher was talking about how we shift from vertices to vertices and also about some slack variables. Do you have a video for that, Sir?

[@tanmaysharma3869]

This was really helpful. Thank you so much!

[@Alex-xh9kv]

You explained it far better than my college professors...16 years ago....

[@imranq9241]

Given any set of constraints are there algorithms that can calculate the optimal point efficiently using simplex geometry ?

[@mathapelongwepe2652]

The only linear programming tutorial that made sense🙌

[@eoncatalyst]

Finally, a good video on the topic!

[@dlerosman6183]

Thanks for the nice explanation.

[@anatolystrashkevich7621]

very comprehensive, thank you

[@vickdeem]

Amazing! Nice explanation.

[@ogunsadebenjaminadeiyin2729]

You really did justice to this topic in a brief time.

[@DrTrefor]

Thank you!

[@mohamudmohameddaar48]

Free Great lesson, Thank you

[@jzcpan]

Is there a video explaining for LP problems with >3 variables? The graph visualisation method would be extremely difficult with more variables. Thanks!

[@kyloren2373]

A give the perfact examples for one to understand each and every bit of topic you introduce.🙏

[@fugoogle_was_already_taken]

You sir, are a lifesaver. Already saved me on multivariable calculus last semester, now saving me on optimization. Thank you!!

[@DrTrefor]

So glad I could help!

[@tivokio]

Thank you! Preparing for a college course after 10 years of not doing math...I have 2 months to prepare haha, wish me luck!

[@user-or7ji5hv8y]

Great explanation!

[@galitna]

Hi, where did you get the figures from your solution at 8:58? thanks

[@TravisDawkins]

Great Video. I had to Subscribe!

[@nosms6581]

I have a question Dr. Brazzet why we need to construct a branch of knowledge i.e linear programming to deal with optimization problem when we have calculus methods like derivatives and Lagrange multiplier etc...

[@Gabi_0048]

I came here to learn about the Simplex Method, but I stayed because of your amazing T-shirt

[@sakhawathossain3362]

But why did u mention 'simplex' word here if it doesn't have any usage????

[@anunknowncommenter7013]

How did he get the value of two Y??? 20- 5 divide 4 times x 10- x divide 2

[@proHannuTorrekens]

Only in this case is the middle point maximum. It is very possible that the maximum actually lies on the axis. If the Isoprofit line has a steep enough slope max will be at y=0. If it's almost horizontal then max will be at x=0.

[@domingoalvarez3984]

Do you have more videos on this topic of linear programming using the simplex method using tables

[@zamzam9031]

This is really awesome....thanks!

[@thomasLMK]

Very clear in explanation.

[@ossahmadrezaazimikohnabi5108]

I love you're T-shirt 😂

[@ossahmadrezaazimikohnabi5108]

@Wilson Go Yeah 😂 but believe it or not here in Iran we learn these things in highschool! I was so happy when I realized I don't need any college algebra course or precalculus when started to learn online.

[@Klarpimier]

*your I’ve never seen it go the other way

[@lailaabidi5734]

السلام عليكم. اشكرك على الدرس. Alsalaam Alikum.. Thank you.

[@wjrasmussen666]

Can you suggest books that might have this type of problems?

[@lovebroman9335]

What can linear programming do that you cant do with lagrange multipliers?

[@sitarabatool585]

great job! nice teacher

[@imranq9241]

Is this related to convex hull problems at all ?

[@xolanikhumalo9267]

nice vid!very informative

[@jordanbarry3212]

Really nice presentation and great production. It appears that you refer to the region as concave, but I'm not sure that is correct. I believe it should be convex since the set of all feasible solutions should form a convex set. Additionally, I don't think you can guarantee solutions in the way you presented in a concave region of the plane.

[@yash1152]

7:00 4 vertices - due to 4 constraints 11:13 anhhh, the concept of *iso-line* is cool - i wanted some similar line/curve too when i was studying this chapter (Senior School) but didnt spend much time to think it out. But yeah, it makes many things much easier to communicate too.

[@DrTrefor]

So often this is taught purely algorithmically, but the geometric idea is so cool!

[@achrafcherkaoui1566]

hi dr from where you got your t-shirt

[@skripten6189]

Excuse me sir, where did you get your tshirt from? I want it :)

[@christinalafaber5060]

Great video ❤❤

[@rayondaitel]

I love your shirt 😂 thank you for the lesson :D

[@przemyslaw568]

How to compute (x,y) when c = $1000?

[@nour_hisham]

LOVE THIS VIDEO💗💗💗

[@charlieobimbo8310]

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

[@lukewitherow6380]

Yeah and you can’t have 10/3 tables

[@mumujibirb]

ILP should be used here

[@charlieobimbo8310]

@@lukewitherow6380 Exactly!

[@lilmonix3957]

what if a table makes 1$ and a bookcase makes 1000$? is optimizing the use of resources affects the profit? help im confused

[@christianevans5471]

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.

[@vladfeldfix7825]

So if I have 8,000 vertices I have to calculate 8,000 times to find the best vertex?

[@leonardoluistorresvillegas6443]

I just have to say, excellent, this video is excellent

[@DrTrefor]

Thank you!!

[@lailaabidi5734]

Please if you have lecture. About simplex lpp method.

[@derekburm]

Love the shirt!

[@owendebest4183]

I WANT YOUR T SHIRT!!! I LOVE IT

[@DrTrefor]

Haha I love it so much:D

[@abuzerbazuka]

Thanks a lot!!

[@moeal5110]

Would you please do a video explaining steps for solving the simplex method, not using graphs

[@hishamabdeltawab5868]

From where can I get a shirt like yours?

[@wjrasmussen666]

Stupid question. How do we deal with things such as: The availability of lumber and say overtime?

[@Sara-oy6ly]

Best explanation thanks 😊

[@jimbojones8713]

amazing, thank you!

[@swayamkumarpatro776]

Thank you sir... You are always there at the right time for me....🙂

[@swayamkumarpatro776]

I wanted lectures on Linear programming and fortunate that you have made lectures sir.... Thank you

[@DrTrefor]

Glad to hear that!

[@PatiliCanlar31]

How can I find the shirt you are wearing? I love it

[@rahulnarasimhan1669]

Love your shirt, where'd you get it from?

[@solotron7390]

No one will buy a partial table or a partial bookcase. What are the optimum dollars for completed tables and bookcases?

[@bakihanma7705]

help me how did it turned out like that 8:45

[@earlybyrdy]

where can I get that shirt?

[@TitanGriffins]

Awesome!

[@petersisler1398]

The feasible region looks convex to me. Is that so? Also, is the solution not integral values for x and y?

[@DrTrefor]

Oh good catch, yes absolutely convex not concave, I've pinned an explanation about that yes! Indeed this shows the precise location and then can round to the nearest integer depending on the context.

[@MusicalGreen]

Well 10 x for lumber and 5x for labour - somehow x can be used for both lumber and labour? I could not accept anything post that :(

[@walkingturtle6646]

where can I get his shirt? I really like it.

[@jaikumar848]

Great video sir! Are you planning to make more videos on linear programming?

[@DrTrefor]

Thank you! Yes, I do plan to! And move a bit more broadly into different optimization techniques (example discrete as well). However, I'm back to differential equations videos for the next few before I can do that.

[@lukasmiller8531]

That intuition you present about why it should be the vertex not on one of the axis, is that always true? If the iso line had a different gradient, it would hit another vertex at its maximum, right? Or can it never have such a steep gradient?

[@DrTrefor]

The claim is it hits some vertex, so you have to check them all to see which it is

[@marciastenvert1671]

you are AMAZING

[@lastnamenexttime6017]

thanks sir love from India

[@DanielTysonM]

Thanks for the introduction! I find this fascinating, so have picked up Robert J. Vanderbei's book on Linear Programming. Though, I would love to know more from you as well - it would be a nice support to the material. Do you have any other videos, or are you planning to make some in the future? :)

[@DrTrefor]

I don't have more yet, but I plan to update this into a series at some point!

[@earthtotracee]

@@DrTrefor I hope you do more of these soon!!

[@asrajan55]

I love the t-shirt! Where can I get one?

[@baqerghezi1342]

9:27 Do x, y should be intgeres since we're talking about table/ shelves?

[@DrTrefor]

Yes, and we need to only accept integers for physical reasons we can find the "exact" answer and then search nearby to find the integer solutions, that works perfectly well.

[@flynnlaurie5722]

i like the video! but how did you get x = 40/3 = 13.33 and y = 10/3 = 3.33 in the computing the maximum section? i'm having a hard time figuring it out

[@charlieobimbo8310]

He took the two equations 5x + 4y = 80 10x + 20y = 200 and solved them using the substitution method, i.e. by making y the subject of the formula for each equation, and then equating the y's to eliminate the y's. And after solving for x (i.e. x=40/3), he got the value for y by using one of the equations which had y as the subject of the formula. Prof. Charlie Obimbo

[@krishnavbajoria7742]

Thank you!!

[@TrinityTwo]

And to think I racked my brain finding maximum and minimum values through differentiation.

[@DrTrefor]

Right?!?

[@TrinityTwo]

Where the hell were you when I struggling with Calculus to the point that I gave up?