@@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
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.
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!
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.
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!
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...
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
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...
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.
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
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
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.
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.
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.
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!. :)
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
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.
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.
@@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!
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 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.
Is there a video explaining for LP problems with >3 variables? The graph visualisation method would be extremely difficult with more variables. Thanks!
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...
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?
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
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?
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.
Did you say that the optimized solution involves making 1/3 of a table and 1/3 of a bookshelf?? This is why I hate business math classes. These word problems that are supposed to make things clear ignore bits of intuitive sense, but they don't tell you up-front which bits of intuitive reality to ignore. Am I the carpenter who is definitely NOT going to make 1/3 of a table? Or am I mathematician who doesn't care about integers? When I do this bookshelf problem on a test and come up with 1/3d of an extra table & bookshelf in the answer, I'm going to assume that I misunderstood and did it incorrectly, and *I'm not going to learn math! I'm going to second-guess myself for eternity*
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
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.
At the very beginning, I don’t see how you’re translating the problem into formula correctly. If X is the number of tables and Y is the number of bookcases, then 10 X is not the amount of lumber for one bookcase. It would be 10 completed bookcases. No?
I really liked the video. However, you showed how to operate with 2 things (n tables, n bookshelfs), what if you have multiple things like (x1,x2,x,...,xn) certainly it is not possible to visualize such function but can you still solve it algebraically?
**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
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 :)
you channel is absolutely amazing, just wanna say i learn so much from watching it. thx for sharing your knowledge.
Glad you enjoy it!
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.
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 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.
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!
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.
How did he get the value of two Y???
20- 5 divide 4 times x
10- x divide 2
Brilliant video. Thank you professor!
Glad you liked it!
very comprehensive, thank you
Today I learned that a carpenter can make and sell a third of a table
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
But why did u mention 'simplex' word here if it doesn't have any usage????
I hope professor Trefor Bazett could cover Convex Optimization in the future. Study with him is really energetic and engaging
I just have to say, excellent, this video is excellent
Thank you!!
I think this is NOT SIMPLEX method. It seems graphical method
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!
Excuse me sir, where did you get your tshirt from? I want it :)
This is definitely the standard method not the simplex method.
Coming from an economics background this makes so much sense. I now know the math behind the concept of equilibrium 😄
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...
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?
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
thanks sir
love from India
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...
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? 😎
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.
Holy shit, thank you! Had to take one in my senior year anyways, might as well just preview for fun
Great explanation, you saved my studies today. Please, keep making videos
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!
Where can I get that amazing t-shirt?
Found it!!
Look for "algebra dance shirt"
If you give someone 1/3 of a table do they pay you $60 or tell you to go away
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.
how are you gonna make fraction of tables and bookshelves. :D. nice video though
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.
@@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.
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.
How about the simplex method sir?
This method is called the simplex method:)
Good morning DR I honestly need help on linear programming 😭
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!
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!. :)
Yes!
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!
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
How can I find the shirt you are wearing? I love it
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.
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?
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.
@@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!
@@DrTrefor it's already 9 months
I love your shirt 😂
thank you for the lesson :D
That's a pretty funny shirt you got there.
Love your shirt, where'd you get it from?
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.
U're the best. U just save me hours of head breaking maths
I WANT YOUR T SHIRT!!! I LOVE IT
Haha I love it so much:D
Thank you! Preparing for a college course after 10 years of not doing math...I have 2 months to prepare haha, wish me luck!
this is amazingly simple in comparison to what i was looking for which is the actual simplex algorithm
Thanks a lot!!
Tx for the lecture 🙏
You're most welcome!
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.
Just forgot the simplex method ...
Is there a video explaining for LP problems with >3 variables? The graph visualisation method would be extremely difficult with more variables. Thanks!
Given any set of constraints are there algorithms that can calculate the optimal point efficiently using simplex geometry ?
I love your shirt.
What am I missing here? Surely both x and y have to be integers otherwise the problem makes no sense in the 'real world'
oh absolutely, you just use the exact values and then move down to the nearest feasible integer
I think that would make it a "mixed integer linear program"
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.
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...
i love the shirt. How can i get it?
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?
At 9:53 its 2000 right? because 180(0) + 200(10) = 2000?
You are right it should have been 2000
A give the perfact examples for one to understand each and every bit of topic you introduce.🙏
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
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 :(
what if a table makes 1$ and a bookcase makes 1000$? is optimizing the use of resources affects the profit? help im confused
My Brother where is simplex method, You just added there only for show🤦🏽♂
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?
Does he even talk about simplex method ? lol
Thanks so much!!!
This is a great video, but the title says "Simplex Method" and you only did the Graphical Method...
I want that shirt!!!!!!!!!!!!!!!!!!!!!! (will it considered cheating if I wear it to test?) who can find it please share link
Do you have more videos on this topic of linear programming using the simplex method using tables
Seeing you in this explanatory video adds zero value in my opinion. In fact, i found it a bit distracting
No one will buy a partial table or a partial bookcase. What are the optimum dollars for completed tables and bookcases?
nice vid!very informative
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?
The claim is it hits some vertex, so you have to check them all to see which it is
So if I have 8,000 vertices I have to calculate 8,000 times to find the best vertex?
Please come to my university and teach us , your teaching method is awesome😍
9:27 Do x, y should be intgeres since we're talking about table/ shelves?
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.
Did you say that the optimized solution involves making 1/3 of a table and 1/3 of a bookshelf?? This is why I hate business math classes. These word problems that are supposed to make things clear ignore bits of intuitive sense, but they don't tell you up-front which bits of intuitive reality to ignore. Am I the carpenter who is definitely NOT going to make 1/3 of a table? Or am I mathematician who doesn't care about integers? When I do this bookshelf problem on a test and come up with 1/3d of an extra table & bookshelf in the answer, I'm going to assume that I misunderstood and did it incorrectly, and *I'm not going to learn math! I'm going to second-guess myself for eternity*
You don't care about integers because you work more than 1 period. If you can make 13.333 tables in 2 weeks, you can make exactly 39 in 6 weeks.
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
Thank you Dr. Trefor, I was so confused in the lecture, your video is so nice and clear!
The feasible region looks convex to me. Is that so?
Also, is the solution not integral values for x and y?
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.
cannot move eyes away from your T-shirt.
I think that I'm getting dumber and dumber... I can't even understand this :/
What can linear programming do that you cant do with lagrange multipliers?
hello, I like the T-shirt, please share the photo, I want to share it to my students in order to have fun remembering the sketches of the functions
At the very beginning, I don’t see how you’re translating the problem into formula correctly. If X is the number of tables and Y is the number of bookcases, then 10 X is not the amount of lumber for one bookcase. It would be 10 completed bookcases.
No?
No. Each table uses 10 units of lumber, so x tables uses 10x units.
I really liked the video. However, you showed how to operate with 2 things (n tables, n bookshelfs), what if you have multiple things like (x1,x2,x,...,xn) certainly it is not possible to visualize such function but can you still solve it algebraically?
The main problem here is that we have to give entire numbers, not fractions.
Your video deserves in million views.
Unfortunately trash videos come in front.
haha I wish!
Just wanted to say you're a wonderful teacher
You explained it far better than my college professors...16 years ago....
Great explanation. Please keep up the good work
There might be some who would prefer "convex" to "concave" here.