Part 2 - Solving a Standard Maximization Problem using the Simplex Method

This video is the 2nd part of a video that demonstrates how to solve a standard maximization problem using the simplex method. References to using the TI-84 plus calculator are also given.

[@BryndonLight]

Wow. This sticks with me better than the 6 hours of lecture I had in class. Thanks.

[@aaronnunez248]

Hello scott, there's a mistake in your matrix. In the first row S2 column, you have a positive 3/5 and it should be a negative 3/5. Because we take -3R2 + R1 --> R1. In this step, -3R2 becomes -3/5 and then we add this to R1 which is zero.

[@sergiodavidricotorres237]

Thought I was crazy

[@vivekdadu]

seriously man!!! only video on youtube which explains the method so clearly

[@mackfangmeier7566]

Know that this vid was made over 10 years ago, but THANK YOU! You have taught me what my professor has failed to teach me after three days worth of lecture in under 20 minutes! Now I see why they call it simple-x.

[@carinadiaz5181]

Sir I think your slack variable sub 2 in row 1 is wrong? I think it should be -3/5

[@Jitters94]

I got that too. I thought I was going crazy.

[@FMAPR]

Hum. Same here. Did you make a mistake here @Scott Elliott?

[@johnndungu2861]

@@FMAPR i had to repeat severally and still got -3/5

[@mrsamot4677]

yeah I got -3/5 as well. bummer that he didn't catch it.

[@greimonst6170]

How do you guys solve for that? I don't get it I'm so dumb.

[@estherrocha150]

OMG Mr. Elliott! I have been banging my head for 2 weeks now trying to understand all this stuff and I just learned it in 15 min with your 2 videos! Thank you multiplied by a million!

[@xMitaaa]

Typically KZbin math videos have never worked for me, but this one has and has taught me more than any professor I have had in my past five math courses, thank you.

[@jigneshmardania6136]

From your first video, you said we have to make the 3 to be zero, so you gave the formulae -3R(2) + R(1) gives row 1. But for the slack variable s2 i get -3/5, rather than 3/5..? In our exams we have to do all calculations by hand so our calculators dont have matrix functions.

[@Mcecil772]

YES

[@tkzsfen]

how come i stay in lectures and listen hours and hours of this and then i come here and understand everything in just 10 minutes. why the hell do i pay the university when the teachers can't teach me a thing, unlike you Scott. Thanks a lot!!!

[@Travinobabino]

Your videos are so much more effective than going to lecture. Thank you.

[@deepanshumolasi7151]

Thx for keeping everything simple , idk why people don't keep it simple like you

[@ipod0junkie]

Thank you so much. I have been trying to get a grasp of this method from my textbook since many days. Our teacher didn't explain it properly either. You've made it so easy for me. I owe a part of my Math grade to you. :)

[@cirenosibor]

Thanks, I've got an exam in an hour, and this was the only thing I couldn't work out how to do. You taught it better than my teacher for sure.

[@niknuranis1591]

Thanks sir ! it's help me a lots since 15 hours I spent on my lecture notes, I couldn't understand much. but by this simple video I just only need about 15 minutes. Wish me luck for my exam next Tuesday.

[@adambarentine6058]

Thank you so much. This is the only video I have found that actually helped me understand how to pivot. Good shit, man.

[@ensign_jim2633]

Thank you so much. I have been struggling with the simplex method and ones friends can only help you so much (since most of them are in the same boat as i am ). Really appreciate it

[@redietwudiye9159]

2021 still using this channel thank you

[@AjaxNotFrancis]

Thank you- you helped me have a better understanding of the simplex method and upon doing it on my own I got the right optimal solution.

[@BrendonWilliams]

Awesome, thank you. My text-book over-complicated this with many seemingly irrelevant information. It's basically just more specific row operations!

[@albertobarbosa9778]

Brendon Williams Algorithm books always need to prove the correctness of algorithms like this. That's why it seems over complicated, because on books there's a lot of theory involved, which is more directed towards mathematicians, if you're in computer science its most likely irrelevant.

[@zogenie]

thank you! So very helpful. I have a quiz tomorrow and I actually feel confident because of this.

[@takyc7883]

THANK YOU FOR EXPLAINING SO SOFTLY

[@sofiamodesto3094]

Hi, how do you choose the non basic vars at minute 3.20?

[@n3onis]

Looks like the columns that only contain a single 1. I guess you figured it out in 6 years tho

[@savvaskastrinos8817]

@@n3onis you saved me a lot of time trying to figure that out

[@danielrowan4251]

I was gonna ask the same, so cheers

[@Helectic]

@@n3onis I appreciate you, couldn't figure it out for the life of me.

[@XAeirosX]

Thank you so much! This has helped me tremendously, and i appreciate you doing this for us. Bravo to a real TEACHER.

[@scottrelliott]

@fastjunkie831 They are non basic because they are not unit columns (a column of zeros except for a single 1). In regard to what it means, it tells us that the value of the non basic variables must be zero.

[@scottrelliott]

@vellerefondis Sorry, not quite sure I am following you. I think it is correct. After performing 1/5 R2 --> R2, we take 10 R2 + R3 --> R3 So the last entry in the x3 column is found by 10 (1/5) + (-7) = 2 + (-7) = -5 Maybe I'm not quite understanding your question. x3 is non-basic in the final tableau because it is a not a unit column (a unit column has all zeros except for a single 1).

[@cornelio78]

Imagine I had to learn this just for the sake of a particular subject and then forget it afterwards.

[@parsadorbeigi3166]

Thanks man! You saved me lots of time and few marks! I was about to get mad! Couldn't figure out how to find the final solution!

[@MarinVillalpando15]

Ooh, I finally get it now. So pretty much, any column with a value of 1 by itself is then matched up to the far right numbers. Any column with a value other than just 1 is immediately zero.

[@mohdrazif777]

Thanks man. My lecturer books answer the question using simplex method in 10 pages. When I use your simplex method, I just need one page for the very same question.

[@Dreamstopp]

Thank you so much. Keep the good work..

[@_P2M_]

Thanks for the videos. However, what is the purpose of the z column? It has all zeroes in the first three rows, so it will not get affected by this process. It's just completely redundant.

[@galax574]

Hi, greeting from Hong Kong. This tutorial video is way more effective than my boring lectures. I've done my exam paper today about Simplex Method and I have unfortunately come across some problems. Could anyone please help? (1) If the objective function has two equal coefficients, say maximize Z = 5w + 5x - y, you will end up having two coefficients of "-5" in the tableau (one from variable w and one from variable x), which one should be chosen as the "most negative indicator"? (2) If the objective function still contains negative element(s) after several row operations, do I need to redefine the "most negative indicator" from the current objective function in the current tableau and then continue implementing row operations? (3) If the objective function contains not only variables, but also a constant, what should I do? For example, the objective function is given as Z = 5w + 2x - 10y + 4, how should I deal with the constant term "+4"? Thanks for replying.

[@zum4342]

At 3:19, what do you mean by unit columns?

[@siddarthkumars6781]

Great video .. Thank you so much !! Understood the problem in no time !!

[@khaledaq4947]

ty so much Mr.Elliott!

[@devinedirisuriya8340]

this was very helpful .thanks

[@MiracleIsMyName]

I can't hear why you say x2, x3, and s2 are Non Basic. Could you clarify?

[@MiracleIsMyName]

Thanks! I got it

[@KingDuken]

+Miracle Jacobs Nonbasic means there's no easy solution. Since there were two coefficients for the same variable, it would be considered nonbasic. So that variable, when you optimize it, it would be 0. Like x2=0 because there was more than one coefficient that did not equal to 0. And since x1 had a 0 and 1, it was considered basic because there was only one coefficient for x1 and it was easy to solve for x1. For every nonbasic variable, you can cross out that column and just say it's equal to 0. This will also help you see how easily you can solve for other variables that are basic. I apologize for any bad English. It's not my first language haha. But I hope that makes sense.

[@MiracleIsMyName]

Thanks *****​

[@jenozen7928]

you sir' are a god!

[@MrYachtie]

Very helpful, thank you! I liked the awkward ending!

[@nicole-oe3vu]

Thank you for this!! I finally got it

[@iramrizvi7485]

That was great sirè. Very helpful, thankyou!!!!

[@MgmailcomAmifShadin]

Love:'(

[@SanjayCNair]

Hey Thanks so much, your explanation is so precise and simple it really got me sorted on this Simplex thing. Thanks again. I have got all the basics of it and also solved it myself and luckily i got the right answer. Thank you. :)

[@Laenthor]

what makes a variable basic or non-basic? Did I miss something here? I think it's too late to even get a reply, my exam is in an hour...

[@TBadalov]

Did you pass the exam?

[@Laenthor]

um, I passed the class, but I think I had like 50% on the exam...

[@michaelcus734]

i have exam on this tomorw please pray for me

[@mun-munanimation7271]

I hope you did good, I have the exam tomorrow.. DID you pass?

[@Caitlynws1644]

thank you so much for these videos, you're a life saver

[@kjman]

How did you get a positive 3/5 instead of a negative 3/5 for the first row and the forth column in the beginning of this video?

[@smarakiswagatika2681]

yes it will be negative only

[@kuro8521]

Thank you so much sir💚💚

[@patrickchula]

THANKS! I couldn't keep up with my professor so I didn't catch everything he said in terms of why differnt things were selected.

[@treasuringlife18]

I m sorted now...thanku for such an easy explanation...

[@zhengbichengwang7794]

Bro may I know why S2 is 3/5? is should be - 3/5 isn't it?... -3 * 1/5 + 0 I'm a bit confuse...

[@HiepNguyen-ud8qe]

you saved me!!! many thanks.

[@princesoni2776]

Thanx very much for telling what is unit column...

[@vicentecfn]

Thank you for the videos! It helped a lot.

[@michaelpetrella8636]

Thank you! Made it much clearer for me

[@jgaricanomena4472]

Btw, in my previous comment, I forgot to thank you for the nice explanation. :)

[@strongmanlin]

Super helpful. Thanks for the tutorial.

[@benedictodhiambo3975]

Thank you have got it well and clear

[@PatricioJeri]

What if all of the result multiplication to determine which row you operate on are negative. Do you choose the one closest to 1 or the one that is the most negative?

[@DingdiMang]

Thank you:) So clear and helpful

[@roselynpaz931]

can someone explain to me how did he get those answers in the second tableua?

[@AmyJeff]

omg, this is so simple actually. thank you very much!

[@brandonsandersvlog3734]

Thank you kind sir! You just helped me Ace my exam :P

[@kyriakos221003]

great explanation. you are perfect. thanks for the video

[@tshepisopower]

THANK YOU!!!

[@nniiiluuu]

thanks for the explanation! amazing job. however, is it possible that you also add the z, s1, s2 in front of the rows and change them according to the pivotcolum? could use an explanation on that as well :). thank you!

[@Dadullah2233]

plz tell me how can we do row operation in FX 199ES calculator or by hand how did u do it when I did the values were different from urs plz show me how dis works thanks from ur wonderful presentation

[@coolstuff8857]

Thanks man! But I have a question, you got a slack of value 2. Doesn't that apply somehow on the maximum value? Or is the slack irrelevant for this question?

[@seller6478]

thankyou for giving me 20 marks in MBA

[@spiker2309]

can the RHS column be negative values at the end? maybe the solution will become negative for one(or more) variables?

[@cz48b1]

Outstanding!!! Thank you so much.

[@JimboDaExtreme]

YOU ARE AMAZING. NOTHING SHORT IF IT.

[@eliezertorres9967]

thanks bro, i've learned a lot! God bless!

[@RazyMon]

Just checking: By unit column you mean column with all 0's and a single 1 in it? Oh, and thnx for clear explanation. We do this in college atm, and our tableau has some extra columns, which requires extra work just to maintain correct values (doing this in exam is a major pain in the a** :D)

[@chrisquarles9219]

this video is fire, thanks

[@wavicle92]

if it was basic, but instead of having a 1 it had 5 say? would you divide the value at the end of the row by 5 or would it be non-basic?

[@Localboy5757]

Bless you, good man.

[@fatimajahangir9073]

Seriously this is so different and easy from the actual Cj Bj bla bla terms method.

[@scottrelliott]

Actually, it does say -7, you just think it looks like a -2. I think if you follow the math, you will see that it really is a -7. I try to make my 2's with a curl at the bottom so there's no confusion. Unfortunately, my 7's do look like a 2 though.

[@scottrelliott]

@RazyMon Yes, that's a unit column.

[@b0ss03]

Omg i didnt know my calculator did all this.! Thanks alot!!

[@sameerkeshavan]

Would you please do a big M method video tutorial? Please and thank you!

[@KidsandKittens217]

How did you get your new bottom row to begin this video with? (I refer to the row starting with -6). Did you add something to the original row (reference row?) in the 1st video (Part 1) that caused this row to start with -6?

[@KingDuken]

+KidsandKarma Sorry if this is a really late reply but maybe it can help someone else with the same question. Let's say that you have an equation: 5x+4y+3z=w For that row, you want to get everything on the same side as w. So subtract. w-5x-4y-3z=0 So this is how you get the row: x y z w -5 -4 -3 1 0

[@88Roshan]

if i pass my math b/c of these videos, i'm sending u a check

[@esirelhalili1667]

Thanks a lot for your help.

[@champ2133]

what do we do if we have equal negative indicators?

[@SmritiSarkar]

thank you for your video.... you've made this very easy.

[@felipedelagarza486]

What if my two ratios are the same? Which one do I choose to pivot?

[@asafel]

great explanation thank you

[@fastjunkie831]

hey man , the R3 row is wrong.after the 10r2+r3->r3 . isn't r2 = 1/5 1 1/5 0 1/5 0 ? you made the calculations with the old r2 row.am i right?

[@henryomeogu6855]

Hi Scott; I tried solving another problem; following your exact same steps. It got to a point where in trying to find the pivot element in the selected pivot column, I had a 0 denominator. The constraint/element on pivot column was 100/0. What can I do in such situation?

[@DanrkspineHaloGod]

You can ignore rows that result in undefined ratios and select the next smallest one.

[@oscar5453]

What program and equipment are you using to make this video? I Want to use it for note taking in class. :D

[@yusefsobky]

So are the variables entering and leaving the basis irrelevant?

[@jgaricanomena4472]

There is an error in 1st video, Row3, column X3 says -2 instead of -7

[@KingDuken]

3:03 I can sense the excitement haha ;)

[@beverlymodise8404]

Wow thank you so much,God Bless

[@jauniuspinelis9533]

thx for clear explanation

[@PunnyPerry]

Tons of Thanks to you :)

[@vellerefondis]

I think there is something wrong with x3, please check it. when you find it -5,i think it's 0 and final 1, i found it 6. Also, why x3 is non basic?

[@nishthashrestha5701]

Thabks

[@ash4957]

Thank u very much.......gr8 works

[@dominicwhyte7033]

Awesome, thank you

[@AngelParkOfficial]

3:12 i dont really get, why they are non basic?