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!
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!
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
@@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 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
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
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!
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.
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).
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.
@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.
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.
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.
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.
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.
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
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.
@@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.
I'm guessing linear programming has already been expanded to include square, cubic, all kinds of exponents? This is the kind of thing mathematicians are not going to leave alone.
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.
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
I was expecting a twist that you will say 1/3 of table is not integer, nobody will buy a half bookcase, then blalabla, the actual/infeasible solution would be..... ....., So i am thinking too much. there is no twist...
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
In Equation 1 if you make only Y Units ,you can make profit of Y=20, when x-valu is 0 Or x is 16 Units ,when Y=0 Let us take we make only Y value the profit is 200y Blung 200(20)= 4000 dollar. Why are taking the option of Two Variable of Table and...
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.
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.
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.
I'm doing advanced physics and I can't even figure out this linear programming. It's starting to piss me the fck off because i've spent hours trying to figure it out and its just not adding up like wtf
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?
**TYPO** At 13:16 when I introduce the Big Idea I call the region concave when I mean convex!!!
I was wondering what a convex region would look like and I see this comment lol
Okay....I understood, thank you
Nice, i was just confused about that and see that now
dude drank 4 cups of coffee before recording the video 😁
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!
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!
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
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
you channel is absolutely amazing, just wanna say i learn so much from watching it. thx for sharing your knowledge.
Glad you enjoy it!
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.
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
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.
@@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
@@vuraxis953 same for some uni courses. you have to do it manually
@@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
@@vuraxis953 interesting, im at cardiff too in data sci :)
this is amazingly simple in comparison to what i was looking for which is the actual simplex algorithm
hands down one of, if not the, best math video I have EVER watched!
Today I learned that a carpenter can make and sell a third of a table
Coming from an economics background this makes so much sense. I now know the math behind the concept of equilibrium 😄
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
Yeah and you can’t have 10/3 tables
ILP should be used here
@@lukewitherow6380 Exactly!
Thank you Dr. Trefor, I was so confused in the lecture, your video is so nice and clear!
U're the best. U just save me hours of head breaking maths
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!
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
I hope professor Trefor Bazett could cover Convex Optimization in the future. Study with him is really energetic and engaging
Just wanted to say you're a wonderful teacher
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.
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.
Holy shit, thank you! Had to take one in my senior year anyways, might as well just preview for fun
The only linear programming tutorial that made sense🙌
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).
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.
I love you're T-shirt 😂
@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.
*your
I’ve never seen it go the other way
I WANT YOUR T SHIRT!!! I LOVE IT
Haha I love it so much:D
You explained it far better than my college professors...16 years ago....
I came here to learn about the Simplex Method, but I stayed because of your amazing T-shirt
You really did justice to this topic in a brief time.
Thank you!
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.
So often this is taught purely algorithmically, but the geometric idea is so cool!
Great explanation, you saved my studies today. Please, keep making videos
Finally, a good video on the topic!
And to think I racked my brain finding maximum and minimum values through differentiation.
Right?!?
Where the hell were you when I struggling with Calculus to the point that I gave up?
Brilliant video. Thank you professor!
Glad you liked it!
Great explanation. Please keep up the good work
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.
You sir, are a lifesaver. Already saved me on multivariable calculus last semester, now saving me on optimization. Thank you!!
So glad I could help!
Loved your lecture and your T-shirt
Thank you! Preparing for a college course after 10 years of not doing math...I have 2 months to prepare haha, wish me luck!
A give the perfact examples for one to understand each and every bit of topic you introduce.🙏
I just have to say, excellent, this video is excellent
Thank you!!
very clear. You nailed it.
really great video on the concept
very comprehensive, thank you
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.
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.
If you give someone 1/3 of a table do they pay you $60 or tell you to go away
How did he get the value of two Y???
20- 5 divide 4 times x
10- x divide 2
"Board feet" are the carpentry unit. :) And Wonka might buy a third of a table!
that reveal at the 8:04 mark was exciting
That's a pretty funny shirt you got there.
This is definitely the standard method not the simplex method.
Your video deserves in million views.
Unfortunately trash videos come in front.
haha I wish!
I love your shirt 😂
thank you for the lesson :D
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
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.
Not if your wood is constrained to 200.
Great video sir! Are you planning to make more videos on linear programming?
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.
This was really helpful. Thank you so much!
thanks sir
love from India
Please come to my university and teach us , your teaching method is awesome😍
Amazing! Nice explanation.
Great explanation!
Very clear in explanation.
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!)
Did you find out where to get the T shirt ???
@@billfitz6246 No, I only found one super expensive 😢
@@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.
But why did u mention 'simplex' word here if it doesn't have any usage????
great job! nice teacher
nice vid!very informative
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?
I think this is NOT SIMPLEX method. It seems graphical method
I'm guessing linear programming has already been expanded to include square, cubic, all kinds of exponents? This is the kind of thing mathematicians are not going to leave alone.
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.
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
Thanks for the nice explanation.
السلام عليكم.
اشكرك على الدرس.
Alsalaam Alikum.. Thank you.
I was expecting a twist that you will say 1/3 of table is not integer, nobody will buy a half bookcase, then blalabla, the actual/infeasible solution would be..... ....., So i am thinking too much. there is no twist...
That is integer linear programming, an advanced form of this technique. Go ahead check it out ;)
LOVE THIS VIDEO💗💗💗
Free Great lesson, Thank you
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
are you ready bro? 😎
My Brother where is simplex method, You just added there only for show🤦🏽♂
cannot move eyes away from your T-shirt.
This is really awesome....thanks!
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
In Equation 1 if you make only Y Units ,you can make profit of
Y=20, when x-valu is 0
Or x is 16 Units ,when Y=0
Let us take we make only Y value the profit is 200y Blung
200(20)= 4000 dollar.
Why are taking the option of Two Variable of Table and...
you are AMAZING
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.
Shouldn't x and y be integers? 13 whole tables, and 3 whole bookcases in 77 hrs, making 2940?
Absolutely, this exact value needs to be rounded to the nearest feasible integer in a real setting.
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.
Great Video. I had to Subscribe!
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.
That’s cool T-shirt tho!
I'm doing advanced physics and I can't even figure out this linear programming. It's starting to piss me the fck off because i've spent hours trying to figure it out and its just not adding up like wtf
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?
Would you please do a video explaining steps for solving the simplex method, not using graphs
Thank you sir... You are always there at the right time for me....🙂
I wanted lectures on Linear programming and fortunate that you have made lectures sir.... Thank you
Glad to hear that!
thank you..
Thank you!!
No one will buy a partial table or a partial bookcase. What are the optimum dollars for completed tables and bookcases?
I love your shirt.
How can I find the shirt you are wearing? I love it
Thanks a lot. ❤️
You're welcome 😊
Best explanation thanks 😊
Do you have more videos on this topic of linear programming using the simplex method using tables
Excuse me sir, where did you get your tshirt from? I want it :)