❖ The Simplex Method and the Dual : A Minimization Example ❖

[@aishvetorah5704]

I'm gonna make a part of graduation speech about you saving student lives.

[@patrickjmt]

+Katsuragi Keima ha, thanks :)

[@georgewekesa1380]

Most definately

[@AsmaaMohamed-kr1dm]

Yesssssss he is amazing in his explanation

[@Hud_Adnan]

did you do it ? ( I'm just curious )

[@aishvetorah5704]

@@Hud_Adnan i graduated online by forced. I cried. They just show us our pictures online that we finished the course then boom done. ;_;

[@runnereatscow]

patrickJMT you saved me when I was getting my general ed math courses. Now once again, you are saving me for my Algorithms class :)

[@peteshramkop.e.4211]

Awesome job mate. It’s been 20 years since I looked at LP since grad school... who knew it would become so relevant to everything we do today 🧐

[@vishalchoure1993]

This was so much easier to understand here than in school. Thank you :)

[@nikkovincegonzales2758]

I chose Y2 as the pivot column in the initial table and got the result in the next iteration. Got lucky I guess, thanks Pat. Your method is faster than the one we were taught.

[@rajuacharya7839]

I really love your working style. Its so simple and easy to understand. Thank you for this video. Love from 🇳🇵 Nepal

[@heavencalling3808]

I've really understood the whole process it's much easier. The fact that I've not seated in any lectures for this semester because of lockdown and no meeting but I've understood as though I was in class and paharps much better than in class. Thanks 🤝🤝🤝🤝🤝

[@vinayaknayak6383]

Thanks a lot for making this video, Patrick!!Just one suggestion, if in the first step, you select the element in the second column or the second column's -8 as the pivot column, then you directly land up at the final matrix (17:50 in the video).

[@nuElevenGG]

thanks! i'm sure a lot of people will find this helpful. maybe you can do a video on the geometric interpretation of the simplex method?

[@rajendramisir3530]

Thanks Patrick. Nice review for me. I learned about the Simplex method in Finite Mathematics 28 years ago in College.

[@iqrandiamalik2881]

Loved it😊 even after 5 years, it still helped

[@gogvale]

I have no idea why this works, but thanks. You just saved me from my exam tomorrow ♥

[@iDramex]

after finishing Math courses I lost hope of seeing you again until I came across this video in an operations research course.

[@hencodelange9289]

I just caught up a week of class 2 hours before the test, thank you

[@Graywolf116]

Came looking for insight into Dual vs Primal problems for ML hw, left with a greater respect for LinAlg and an idea how row ops can be made into an algorithm. Thanks!

[@xoppa09]

it would be nice to put all the simplex videos into one playlist. nice video ;p

[@tobyto4614]

I read the brilliant's steps on performing this, it is trying to solve it from bottom to top, which is hard to understand. This one explains it very clearly on how the operations go. :D

[@austinfairris4332]

Awesome video. Can I ask when youre turning the problem into a maximization and taking the transpose, what if the matrix is not square like it is here? Will it still work if say we take a 5x3 matrix and transpose it into a 3x5? Thanks

[@mercymwanza7715]

😄😄I like where you say this is fun😆 it is fun when you know what you are doing, just like my lecturer always says,"have the confidence. "

[@notmimul]

I really like your energy and way of explaining it. from A-Z

[@avaolsen1339]

Great video, Thank you! Question: at 19:52 you said the goal is to have zeros everywhere else. once you get rid of negative numbers, you would get a solution. Could you please clarify on that? what do you mean by 'have zeros everywhere else'? thank you.

[@tutsyb26]

You are the definition of a life saver..thank you Patrick!

[@comfortinnsuitesmiller6588]

Thank You So Much For Making Videos. it helps a lot to understand complex problems.thank you so much sir..

[@jaysorenson2662]

I first used this technique back in 1968. Used it to solve resource allocation in banking. One can also use it for goal seeking.

[@pootlovato8285]

Thats so cool how applicable this method is, why i love matrices. It was first used in 1947 when there was a scheduling problem with the Berlin airlift

[@warank]

that was even an easy explanation for a high-schooler(which is me) thanks a lot

[@patrickjmt]

glad i could help!

[@alejandroservin1432]

I had an economics teacher who says y1 the way you do, god does that really urk me 😅

[@tobiaskaufmann5205]

Why are you writing 1 at 2:05 when later in the simplex starting table you replace it with 0 after transposing the matrix? (as it produces the wrong solution when you don't writ 0 instead of 1)

[@Hoo852r]

you are an ass saver I swear!! nothing got me through hard major courses but your videos ! THANK YOU !!

[@patrickjmt]

pjmt, the ass saver.

[@hassanhashemi6478]

dude, i love you.

[@AbdulraufuMashaka]

Another example please 🥺

[@小小豬-u3f]

Correct me if I was wrong. Since every row of P column is always 0, so no matter what oprations it has been done, the last row is always 1, (there are no cases that the last row will be chosen as the "pivot row" and apply it opration to the other rows), which means, this column is completely useless and therefore could be omited.

[@manojkumarhk5696]

When you took X1 and X2 as slack variables, how did you choose the corresponding inequality? Because if we exchange X1 and X2, I might get X1=0 and X2=8; which can't be right!

[@shereenzalloum6909]

Patrick your such a life saver omg 😭 can you please make a video about the two-phase method & Big M method? please please please my exam is on the 20th.

[@patrickjmt]

i will look into them!

[@shereenzalloum6909]

I would really appreciate! I don't understand from my teacher because I moved to a country that doesn't speak English and I don't understand half the things he says... anyways thank yooouuuuu Pat! :D

[@amyl3766]

Bless you and your family.

[@redjon0999]

OMG now i am clear. thank you so much bro,

[@muathkawther662]

Question.. in the maximization problem videos you said that we should write the slack variables also on the left side of the matrix as we solve the problem, and change/replace them accordingly whenever we perform any operation during our solution.. why didn't you do the same thing in this minimization problem??

[@waleedahmed5708]

Muath Kawther yah I had the same question

[@uhavebeen]

I had the same question as well, I think maybe because it's a dual problem/maximization it's different?

[@bhangi]

can someone answer thsi question? please?

[@atkinsonmachingauta4034]

I think the same process still applies, only that here he was not really concerned with writing the slack variables since its a dual problem. This therefore means that even if we solve the problem, it is easy to identify the replacement that was supposed to be done because its an either or situation.

[@athanasiakaragianni1447]

so what is the actual solution? the one he did or the one with the other way he showed in the previus videos?? (8,0,8,0) or (0,3,0,3) ?

[@scottsimpkins7894]

I think the last step should result in x1 = 10 and P = 30. With that -2 hanging around under x1 you never get an x1, x2 unity matrix. If you don't mind clarifying...thank you.

[@purpleboxersrocks]

I wish you were my lecturer because I'll definitely get what you were saying. Provided of course, if the whiteboard was a zoomed in screen of your hands and sharpie markers instead xD

[@badAtPickingUsernames1988]

8:28 Are there any circumstances where you don't take the smaller value? I saw an example done where it is a minimization problem and it had -32 and 30 in the rightmost column and in the pivot column it had -1 and 5 respectively with 5 in the bottom row. They didn't even explain why they just said you use -1. But 6 < 32. Did they just make a mistake?

[@robiyonas1401]

Why in the other video the values corresponding to the variables were the constants at the outer right of the matrix, but in this video, the variables correspond to the last row.

[@EN-yn2zx]

If pivot is in 2nd row, then do we have to turn the number under it into zero? Or the one above it as well?

[@shsabre5874]

I just wonder after you find the most negtive element during the simplex process, what if there is a negative constant exist. should I pick that the most smaller number? or only smallest divided positive constant is my next target?

[@jasminebactat2436]

what if the matrix you want to transpose is not square? can we just add another variable like Y3?

[@harrisonfok8267]

Yo man thanks for saving my life lol Was stuck on this yesterday for so long

[@invictus_1245]

Thank you man, you make this stuff so easy why does my teacher over complicate these problems?

[@karelsurya4809]

i just realized that he is a lefty lol. kinda satisfying to watch that left hand move around

[@bram3205]

5:23 "it turns out thats what you wanna do" Why? I don't understand why all of this works this way..

[@MiaowJahat]

he said that he already did 5 videos about that part. so, watch that videos first, ok?

[@Plagger]

@@MiaowJahat what if u had 3 variables at the initial minimization problem? u wouldn't be able to fit in a 3rd x3, in the new maximization problem. i also didnt get it

[@sajanamethsarakulathunga243]

you are a hero man ...i love youuuuuuuuu

[@tonyuriano4469]

why is the C value assumed to be 1 and not 0 when filling out the initial tableau? I believe this is an oversight...

[@TheMuteBoy]

Alhamdulilah thank you so much sir

[@luzongomaybinmumbuwa2114]

wonderful presentation

[@saifullah4127]

@patrickJMT please check the solution of the dual program, you got y=(8,0) which is not satisfying constant 1 of the dual problem.

[@pramoudaya7432]

can you explain with 3 variables with greater than equal constraints please?

[@my_religion]

What if the smallest ratio is negative? should we take the row with the least positive ratio?

[@madeIeine]

Okay, around 8:48 how about when it's 3 instead of two? Will I still use 1/2? Or not?

[@jurajhlavek7742]

u would divide it by 3 (1/3). What you need is to get number 1 as pivot, so if you would have there for example 16, you would divide whole row by 16 (1/16)

[@featheredice]

11:18 Kinda confusing, I think you mean three halves plus nine :)

[@GustavoGarufi]

Another question that I've been left wondering, what is the difference between this dual simplex method and the regular simplex method?

[@ahmedyasser9639]

Reqular we search in in objective function for a pivot column, dual we search for the pivot row from the constrain R..H..S

[@ferdaozdemir]

@@ahmedyasser9639 Yes, but why do we take that effort. Why do not use just regular simplex? What is the advantage of converting simplex problem to dual and solving it? I am also trying to understand this.

[@mounaamouna2459]

@@ferdaozdemir we use the dual method to transform the lpp from its current form to the standard form then we can use the algorithm of simplexe and solve the rest of the problem

[@mounaamouna2459]

i hope i said it correctly and clearly

[@rajendramisir3530]

@@mounaamouna2459 I think you stated that fact correctly.

[@ssuriset]

Wait.. so in the dual simplex, you don't have to keep track of your pivot value's column label (on the leftmost of the pivot) and switch it with its row label (on the topmost of the pivot)?

[@brandonc4346]

you are the best , god bless you

[@rimaben2120]

Very well explained, thank u! But what if wheb choosing pivot befor deviding and comparing, what if we have to choose between 5/2 and b 7/0 for axample?! Is this case possible to face..

[@lasharistudio8878]

Please tell advantages and disadvantages of simplex method

[@nyahhbinghi]

isn't there a way to run minimization without transposing and using the dual? Would be nice to address that.

[@fidelio2281]

After u transposed the minimazation problem into maximazation, at the time u want to get zeros on your pivot column, why dont u exhange variables at the left of the tableu as you did every time in your video with the maximazation problem ? It will be a blessing if u answer as quick as you can.

[@allyanamanabat7323]

Is the regular and this dual simplex method the same? I mean does they point out to one answer???

[@Mallorque40]

Can you talk about the Kuhn and Tucker theorem?

[@amodingteddy1877]

Thank you🥰🥰🥰🥰

[@o.biertrinker9649]

I don't know why I find duality so fascinating, as it were more than mathematics, rather art!!

[@fiorella5717]

Could you please tell me what is the goal to change it to maximization?, thanks!

[@MacPSPpro]

Because the simplex method works only for maximization I think

[@Skandalos]

@@MacPSPpro multiplying the objective function by -1 and then maximazing it seems less work than this dual method.

[@shabbirsaifee7497]

Hey, what if there is equality instead of inequalities. How to apply the method in those case?

[@stephenholmes9386]

I'm pretty sure you've messed up but got lucky? You've chosen the slack variables to be the values of x1 and x2... Is that right?

[@Qwevo8]

Thanks so much...

[@RohanSharma-tf3fn]

My question have 3 variables 2 constraints so the matric is 3x4 transpose is 4x3 idk what to do

[@xaoc2nd]

Hello, why don't you use slack variables? And why don't you read your x1 and x2 as the maximization in your table?

[@xaoc2nd]

Oh i understood, that's because you use the dual method to make it more easier

[@hbbn6281]

Thank you very much.

[@patrickjmt]

you are very welcome!

[@balthazar500]

Thank you, you're a Godsend!

[@ezioauditore4109]

watching a day before finals

[@johnberry6077]

Anybody can "jump in" and answer this, if they know the answer. [question]: When you get to the part where he does the _transpose,_ he was working with a _Square Matrix,_ from which a _transpose_ can be formed, very nicely. If, instead, at that step, he had to _transpose_ a *non-* _Square Matrix,_ would his method (for converting a *minimize* problem into a *maximize* problem) still work?

[@johnberry6077]

I think I figured out what you would do *if* the original _minimization_ problem had more than *2* constraint equations. Let's suppose that the original _minimization_ problem had *15* constraint equations. According to the three possible *row operations* rules, you could identify *14* (of the *15* ) constraint equations, add them all together into a _single_ constraint equation, and then you would have _only_ *two* remaining constraint equations (which would fit into the form of being the 2-by-2 _Square Matrix_ that he _transposes._ )

[@christinastanley3938]

Thank you very much :) !

[@patrickjmt]

You're welcome!

[@victoriacharalambous6977]

thank you so much!!!!!!

[@sarahnjoki1655]

what happens when the constant on the right hand side becomes negative

[@seankennethumali4382]

What if there are three constraints? It would look like there are 3 x1, x2, x3

[@randal-ashqar2103]

I need your help, I have homework about dual and primal simplex i cant do it

[@eliteeconomics3158]

what kind of simplex method is this?

[@cgsshshh4255]

can we convert the objective function to max by multiply it by negative 1

[@audryk.7825]

that's what I thought

[@Skandalos]

Whats the advantage of this? Why not just solve the primal problem? Seems just more work to me.

[@IKIN_10]

Can someone please explain why do we use duality in the first place?

[@SequinBrain]

five years too late, but there wasn't the basic variables to the left which were entering and leaving, even though I saw them on your scratch sheet. I was able to figure out what they were anyway.

[@NejatMolla]

Came here looking for copper. Found GOLD

[@sandrasurendran5068]

Thanks a lot !!!

[@bayanalsaraireh4037]

thank you so much .

[@Alexandrusg]

I did everything exactly how you did but my professor said its not a right method to get your X1 and X2?

[@mrsamot4677]

Yeah I thing it's because he used x1, x2 names for his slack variables. I think he should have used his y1, y2 Vals. Can anyone else confirm?

[@addisuberhanuofficial1829]

Wow good job

[@josefsamik3859]

the slakes of the dual are the solutions of the primal ? how ?

[@jon7960]

Not sure if you actually care anymore since you posted this 5 months ago, but there is a theorem called the Duality Theorem that states and proves this.

[@desmondmaluleke3484]

im confused,,why are you doing maximization while the question is requesting you to calculate minimization?????

[@VonDutchyy]

Yeah but he has turned a minimization question into a maximization to make it easier by transposing the matrix, the result is the same

[@lolaalsaadi5708]

Thanks a lot , actually i want to know how to use MM algorithm with phase noise

[@macmoore5452]

why is the slack variable in this the same as the original variable, why not the usual s1, s2

[@macmoore5452]

also the way you pick your x1 and x2 is different from the way we pick them in the previous example(maximization example)

[@ScepticalElephant]

why is'nt x(2) 3?

[@wheyllch2858]

why did you pick the most negative values when it's a mximization problem ?

[@rimaben2120]

Bcz He multiplied the maximization equality by -1

[@yigitsevim1516]

hocam 18.46 da ne yaptınız hocam?????

[@awayggamer]

hi what about i'm blank about this Max z=x1+x2+x3+x4 subject to x1+x2

[@axelfarias3]

X1 = 5 x2= 0 X3= 2 X4=1