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Intro to Linear Programming
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Күн бұрынThis 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 3 жыл бұрын
**TYPO** At 13:16 when I introduce the Big Idea I call the region concave when I mean convex!!!
@SAAARC 3 жыл бұрын
I was wondering what a convex region would look like and I see this comment lol
@georginamuluki2134 2 жыл бұрын
Okay....I understood, thank you
@imranq9241 2 жыл бұрын
Nice, i was just confused about that and see that now
@ikersanchez8222 2 жыл бұрын
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!
@chibby0ne 2 жыл бұрын
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 2 ай бұрын
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.
@MrRomulocunha 3 жыл бұрын
you channel is absolutely amazing, just wanna say i learn so much from watching it. thx for sharing your knowledge.
@DrTrefor 3 жыл бұрын
Glad you enjoy it!
@lahirujeewantha5208 Ай бұрын
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
@Ender7j 2 жыл бұрын
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
@vuraxis953 3 жыл бұрын
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 3 жыл бұрын
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 3 жыл бұрын
@@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 Жыл бұрын
@@vuraxis953 same for some uni courses. you have to do it manually
@vuraxis953 Жыл бұрын
@@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 Жыл бұрын
@@vuraxis953 interesting, im at cardiff too in data sci :)
@tuongnguyen9391 3 жыл бұрын
I hope professor Trefor Bazett could cover Convex Optimization in the future. Study with him is really energetic and engaging
@michaljaros1380 2 жыл бұрын
Great explanation, you saved my studies today. Please, keep making videos
@charlieobimbo8310 2 жыл бұрын
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 2 жыл бұрын
Yeah and you can’t have 10/3 tables
@mumujibirb Жыл бұрын
ILP should be used here
@charlieobimbo8310 Жыл бұрын
@@lukewitherow6380 Exactly!
@dariuszspiewak5624 2 жыл бұрын
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.
@much-love- Жыл бұрын
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
@ningxinzheng4382 Жыл бұрын
Thank you Dr. Trefor, I was so confused in the lecture, your video is so nice and clear!
@KatlegoMmadi Жыл бұрын
Coming from an economics background this makes so much sense. I now know the math behind the concept of equilibrium 😄
@ronhernandez8857 2 жыл бұрын
this is amazingly simple in comparison to what i was looking for which is the actual simplex algorithm
@fugoogle_was_already_taken 3 жыл бұрын
You sir, are a lifesaver. Already saved me on multivariable calculus last semester, now saving me on optimization. Thank you!!
@DrTrefor 3 жыл бұрын
So glad I could help!
@reubensolomon4162 Жыл бұрын
U're the best. U just save me hours of head breaking maths
@ossahmadrezaazimikohnabi5108 3 жыл бұрын
I love you're T-shirt 😂
@ossahmadrezaazimikohnabi5108 3 жыл бұрын
@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 2 жыл бұрын
*your I’ve never seen it go the other way
@yeetonykp4569 2 жыл бұрын
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.
@dilipbarman9322 6 ай бұрын
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!
@owendebest4183 3 жыл бұрын
I WANT YOUR T SHIRT!!! I LOVE IT
@DrTrefor 3 жыл бұрын
Haha I love it so much:D
@IMadeOfClay 3 жыл бұрын
Brilliant video. Thank you professor!
@DrTrefor 3 жыл бұрын
Glad you liked it!
@axisepsilon514 3 жыл бұрын
Holy shit, thank you! Had to take one in my senior year anyways, might as well just preview for fun
@TrinityTwo 3 жыл бұрын
And to think I racked my brain finding maximum and minimum values through differentiation.
@DrTrefor 3 жыл бұрын
Right?!?
@TrinityTwo 3 жыл бұрын
Where the hell were you when I struggling with Calculus to the point that I gave up?
@MossesRoss Жыл бұрын
Just wanted to say you're a wonderful teacher
@yash1152 3 жыл бұрын
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 3 жыл бұрын
So often this is taught purely algorithmically, but the geometric idea is so cool!
@anunknowncommenter7013 2 жыл бұрын
How did he get the value of two Y??? 20- 5 divide 4 times x 10- x divide 2
@tivokio 9 ай бұрын
Thank you! Preparing for a college course after 10 years of not doing math...I have 2 months to prepare haha, wish me luck!
@kyloren2373 2 жыл бұрын
A give the perfact examples for one to understand each and every bit of topic you introduce.🙏
@StokesburyUSA 8 ай бұрын
Wonderful explanation. Thank you for the video.
@sakhawathossain3362 3 жыл бұрын
But why did u mention 'simplex' word here if it doesn't have any usage????
@christianevans5471 2 жыл бұрын
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.
@Gabi_0048 2 жыл бұрын
I came here to learn about the Simplex Method, but I stayed because of your amazing T-shirt
@iloveutubealotandmor 11 ай бұрын
Great explanation. Please keep up the good work
@Alex-xh9kv 2 жыл бұрын
You explained it far better than my college professors...16 years ago....
@ogunsadebenjaminadeiyin2729 3 жыл бұрын
You really did justice to this topic in a brief time.
@DrTrefor 3 жыл бұрын
Thank you!
@sinecurve9999 2 жыл бұрын
This analysis assumes someone values a third of a table and bookshelf equally to a full bookshelf and table. An additional constraint would be to consider only integer coordinates inside the feasibility region.
@lastnamenexttime6017 2 жыл бұрын
thanks sir love from India
@proHannuTorrekens 2 жыл бұрын
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.
@eoncatalyst Жыл бұрын
Finally, a good video on the topic!
@vinayajoseph7025 2 жыл бұрын
Loved your lecture and your T-shirt
@anatolystrashkevich7621 2 жыл бұрын
very comprehensive, thank you
@tanmaysharma3869 2 жыл бұрын
This was really helpful. Thank you so much!
@mathapelongwepe2652 Жыл бұрын
The only linear programming tutorial that made sense🙌
@saisiva5808 3 жыл бұрын
I think this is NOT SIMPLEX method. It seems graphical method
@prashanthkumar0 2 жыл бұрын
really great video on the concept
@rakhshandamujib2793 2 жыл бұрын
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?
@jaikumar848 3 жыл бұрын
Great video sir! Are you planning to make more videos on linear programming?
@DrTrefor 3 жыл бұрын
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.
@xinaesthetic 2 жыл бұрын
I was waiting for the point where you go back to acknowledge the nature of the problem space: the carpenter is not going to make any money for an unfinished item of furniture, so your model needs to allow only for integer values of x & y. (FWIW my reason for looking up simplex method was because the news today in the UK was that school exam students will be given some extra information in advance about which topics will be in the exam papers; simplex method I remember as being the one topic in discrete maths that my whole class had trouble with, and eventually the teacher decided that it looked unlikely to appear in the exam. Unfortunately it did appear in that years paper… I feel like it may have been a different simplex algorithm that we covered, though).
@FactCheckerGuy 8 ай бұрын
The carpenter can finish the product in the next period, so if he can make 13.33 tables in 2 weeks, he can make 39 in 6 weeks. His optimization problem doesn't depend on integer values unless he is constrained to a short period.
@randomdebris 3 жыл бұрын
Shouldn't x and y be integers? 13 whole tables, and 3 whole bookcases in 77 hrs, making 2940?
@DrTrefor 3 жыл бұрын
Absolutely, this exact value needs to be rounded to the nearest feasible integer in a real setting.
@francesccomellas6490 Жыл бұрын
The solution (in the context of integers) is x=12 , y=4 and profit 2960. The solution should be on the border of the "feasible region", but not in a vertex, in this case.
@dlerosman6183 5 ай бұрын
Thanks for the nice explanation.
@georginamuluki2134 3 жыл бұрын
How about the simplex method sir?
@DrTrefor 3 жыл бұрын
This method is called the simplex method:)
@mohamudmohameddaar48 5 ай бұрын
Free Great lesson, Thank you
@leonardoluistorresvillegas6443 3 жыл бұрын
I just have to say, excellent, this video is excellent
@DrTrefor 3 жыл бұрын
Thank you!!
@user-or7ji5hv8y 3 жыл бұрын
Great explanation!
@Dkdkxncnchz 3 жыл бұрын
Lol happy that the moment when i will be doing this course on september i wont need to worry about the youtube teachers at least hahaha
@leonardoscalzi 3 жыл бұрын
are you ready bro? 😎
@danielferreira4005 2 жыл бұрын
That's a pretty funny shirt you got there.
@vickdeem Жыл бұрын
Amazing! Nice explanation.
@xolanikhumalo9267 2 жыл бұрын
nice vid!very informative
@asht750 3 жыл бұрын
Just a quick comment. When writing down the linear inequalities, I don't think it is allowed to have strict inequality signs at all. That's what my textbook says.
@DrTrefor 3 жыл бұрын
The method is fine either way in general, but for a specific problem you have to be careful what exactly it is asking for as to whether the inequalities are strict or not
@millerca1986 5 ай бұрын
this is a great explanation. to expound on the most money concept, you obviously wouldn't make money on 1/3 of a table or cabinet etc. How would you solve that so that the constraints are a whole number? Wouldn't that add another layer of feasibility and give a more accurate representation of money made?
@Bibi_Mbaape 2 жыл бұрын
Where can I get that amazing t-shirt?
@jeanpeuplu3862 2 жыл бұрын
Found it!! Look for "algebra dance shirt"
@ericsperling9724 Жыл бұрын
Your example says the optimum number of tables is 40/3 (13.33) and bookshelves is 10/3 (3.33) but you can't sell partial products so isn't the real optimal value 13 tables and 3 bookshelves? ($180 * 13 tables) + ($200 * 3 bookshelves) = $2,940
@FactCheckerGuy 8 ай бұрын
Well, you can make partial products. If I can make 13.33333 tables in 2 weeks, then I can make 39 tables (exactly) in 6 weeks.
@rayondaitel 2 жыл бұрын
I love your shirt 😂 thank you for the lesson :D
@thomasLMK Жыл бұрын
Very clear in explanation.
@lailaabidi5734 2 жыл бұрын
السلام عليكم. اشكرك على الدرس. Alsalaam Alikum.. Thank you.
@sitarabatool585 2 жыл бұрын
great job! nice teacher
@zamzam9031 2 жыл бұрын
This is really awesome....thanks!
@jzcpan Жыл бұрын
Is there a video explaining for LP problems with >3 variables? The graph visualisation method would be extremely difficult with more variables. Thanks!
@jordanbarry3212 2 жыл бұрын
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.
@nz7467 2 жыл бұрын
that reveal at the 8:04 mark was exciting
@pipertripp 3 жыл бұрын
I love this subject b/c it's so elegant and pretty simple. Is this vid a one-off or does it belong to a playlist?
@DrTrefor 3 жыл бұрын
Hoping to do a little series on optimization techniques, but for the next month or so it'll be a one-off as I head back to finishing off differential equations.
@pipertripp 3 жыл бұрын
@@DrTrefor gotcha. I'll be sure to keep an eye for the other vids in as they appear. The ODE series is brill so glad to hear that you're putting your focus on that. It's been a great supplement to my self-study, so thank you!
@naman4067 2 жыл бұрын
@@DrTrefor it's already 9 months
@moeal5110 Жыл бұрын
Would you please do a video explaining steps for solving the simplex method, not using graphs
@proHannuTorrekens 2 жыл бұрын
This is definitely the standard method not the simplex method.
@civenge1802 2 жыл бұрын
It seems like you can't sell a partially completed product though, so the actual profit for completed products would be $2,940 for that 80 hours worked, still ahead of the $2,880 number.
@davidw2417 4 ай бұрын
However, you can't sell a fraction of a table or bookcase ;) I wonder what the answer looks like if you add the constraint that X and Y are integers? My assumption is that the valid point closest to the vertex in the video that also exists in the feasibility region, at (12, 4), is the solution
@naemishinexuugi3396 2 жыл бұрын
Good morning DR I honestly need help on linear programming 😭
@domingoalvarez3984 Ай бұрын
Do you have more videos on this topic of linear programming using the simplex method using tables
@nour_hisham 2 жыл бұрын
LOVE THIS VIDEO💗💗💗
@jeanpeuplu3862 2 жыл бұрын
I am obsessed by the T-shirt. Offering myself this T-shirt for Christmas. Need T-shirt. Want T-shirt. Get T-shirt. (btw, great explanation, thanks!)
@billfitz6246 2 жыл бұрын
Did you find out where to get the T shirt ???
@jeanpeuplu3862 2 жыл бұрын
@@billfitz6246 No, I only found one super expensive 😢
@jeanpeuplu3862 Жыл бұрын
@@billfitz6246 I finally ordered one: did an image search, ordered a personnalized t-shirt, paid... and never got it, contacted the support, was told to contact the post office, got lazy, no shirt.
@djkosgabby 3 ай бұрын
I love your shirt.
@DanielTysonM 2 жыл бұрын
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 2 жыл бұрын
I don't have more yet, but I plan to update this into a series at some point!
@earthtotracee Жыл бұрын
@@DrTrefor I hope you do more of these soon!!
@TheFarrukhzain 3 жыл бұрын
how are you gonna make fraction of tables and bookshelves. :D. nice video though
@DrTrefor 3 жыл бұрын
haha good point! I even had an explanation about that but cut it for length lol. The exact number tells where to look and then you have to go down to the nearest integer basically.
@TheFarrukhzain 3 жыл бұрын
@@DrTrefor Amazing work. I am binge watching this whole channel after deciding to go back to school for PhD. So grateful for all the effort.
@hannescaesar4820 2 жыл бұрын
Nice video! Just two remarks: 1. At 10:10 , your mixed up the coefficients of the objective function when calculating f(16, 0) and f(0,10). 2. The feasible region is convex and not concave. This is the major argument of LP, so you should maybe put a note!. :)
@FactCheckerGuy 8 ай бұрын
Yes!
@TravisDawkins 2 жыл бұрын
Great Video. I had to Subscribe!
@10Xengineering 10 ай бұрын
This is an integer problem because you can't make half table or bookcase. Your answer is mathematically correct, but not feasible. The actual maximum profit is $ 2,960 for x = 12 and y = 4.
@FactCheckerGuy 8 ай бұрын
No. You can make half a table or bookcase and then finish them the next week. If the carpenter makes 13.333 tables in 2 weeks, he can make 39 in 6 weeks.
@10Xengineering 3 ай бұрын
@@FactCheckerGuy, In Linear programming, there is the idea of integer and mixed integer problems. Having decimals in the final answers doesn't make sense at all. The same thing will apply when talking labor force distribution; you cannot assign work to 1 and half people.
@PatiliCanlar31 2 жыл бұрын
How can I find the shirt you are wearing? I love it
@skripten6189 2 жыл бұрын
Excuse me sir, where did you get your tshirt from? I want it :)
@Alfa1M 2 жыл бұрын
Your video deserves in million views. Unfortunately trash videos come in front.
@DrTrefor 2 жыл бұрын
haha I wish!
@swayamkumarpatro776 3 жыл бұрын
Thank you sir... You are always there at the right time for me....🙂
@swayamkumarpatro776 3 жыл бұрын
I wanted lectures on Linear programming and fortunate that you have made lectures sir.... Thank you
@DrTrefor 3 жыл бұрын
Glad to hear that!
@asrajan55 3 ай бұрын
I love the t-shirt! Where can I get one?
@lukasmiller8531 2 жыл бұрын
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 2 жыл бұрын
The claim is it hits some vertex, so you have to check them all to see which it is
@csabszibabszi 4 ай бұрын
producing 3.3 bookcases and 13.34 tables is not a nice round result :) but the explanation was very good and the video is high quality, so thanks for that
@ace3examcell376 3 жыл бұрын
Sir please upload some content on the Fourier series with real-time Applications
@DrTrefor 3 жыл бұрын
Fourier series actually coming out in one week!
@Sara-oy6ly 2 жыл бұрын
Best explanation thanks 😊
@jimgardner6394 3 жыл бұрын
What am I missing here? Surely both x and y have to be integers otherwise the problem makes no sense in the 'real world'
@DrTrefor 3 жыл бұрын
oh absolutely, you just use the exact values and then move down to the nearest feasible integer
@kiddjmadd 3 жыл бұрын
I think that would make it a "mixed integer linear program"
@christinalafaber5060 Жыл бұрын
Great video ❤❤
@nosms6581 9 ай бұрын
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...
@sandeshgoli1591 3 жыл бұрын
Thanks a lot. ❤️
@DrTrefor 3 жыл бұрын
You're welcome 😊
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