Part 2 - Solving a Standard Maximization Problem using the Simplex Method
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- Опубликовано: 1 окт 2024
- 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.
Wow. This sticks with me better than the 6 hours of lecture I had in class. Thanks.
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.
Thought I was crazy
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.
YES
Sir I think your slack variable sub 2 in row 1 is wrong? I think it should be -3/5
I got that too. I thought I was going crazy.
Hum. Same here. Did you make a mistake here @Scott Elliott?
@@FMAPR i had to repeat severally and still got -3/5
yeah I got -3/5 as well. bummer that he didn't catch it.
How do you guys solve for that? I don't get it I'm so dumb.
seriously man!!! only video on youtube which explains the method so clearly
Hi, how do you choose the non basic vars at minute 3.20?
Looks like the columns that only contain a single 1.
I guess you figured it out in 6 years tho
@@n3onis you saved me a lot of time trying to figure that out
I was gonna ask the same, so cheers
@@n3onis I appreciate you, couldn't figure it out for the life of me.
@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.
I can't hear why you say x2, x3, and s2 are Non Basic. Could you clarify?
Thanks! I got it
+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.
Thanks *****
you sir' are a god!
At 3:19, what do you mean by unit columns?
Imagine I had to learn this just for the sake of a particular subject and then forget it afterwards.
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.
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...
what my professor couldnt teach in 3 months, done in 14 mins ???? uni education is a scam!!!1
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.
@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).
Thank you so much. Keep the good work..
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...
Did you pass the exam?
um, I passed the class, but I think I had like 50% on the exam...
i have exam on this tomorw please pray for me
I hope you did good, I have the exam tomorrow.. DID you pass?
this was very helpful .thanks
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?
yes it will be negative only
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!!!
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.
Thank you so much sir💚💚
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.
Typically RUclips 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.
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!
Thank you!!!!
THANK YOU!!!
Thabks
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?
Thank you have got it well and clear
what do we do if we have equal negative indicators?
2021 still using this channel thank you
Thank you for this!! I finally got it
Your videos are so much more effective than going to lecture. Thank you.
can someone explain to me how did he get those answers in the second tableua?
Thx for keeping everything simple , idk why people don't keep it simple like you
I don't understand how the first iteration/second tableau was made 😭
THANK YOU FOR EXPLAINING SO SOFTLY
ty so much Mr.Elliott!
I want to @ my professor and invite him to watch this video
That was great sirè. Very helpful, thankyou!!!!
Love:'(
No explanation why the numbers changed or why they're suddenly fractions? I did the calculations from part 1 by hand and the the jump in this video with no explanation has thrown me off. Why is the new tableu like that??
Hmmm... looks the same to me. Maybe this is not the "Part 2" video you were expecting?
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?
you saved me!!! many thanks.
Seriously this is so different and easy from the actual Cj Bj bla bla terms method.
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?
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)
@scottreliott i finally get it wooooooooooooo now all i have to do is practise it xD man thanks a bunch for these videos tho one thing i did not like was the begining part of part 1 were u got X subscript 1,2 n 3 were did those come from? and why did the objective function have them?
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
Thank you so much. This is the only video I have found that actually helped me understand how to pivot. Good shit, man.
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?
I understand the simplex method, but I hate it when you make mistakes, even if they are very minor ones. Please avoid this in the future, because it's very frustrating and slows down my learning process
@scottrelliott please explain to me why x2 x3 s2 are non basic.what does that mean?how do i figure that out?
WHY U CUT THE VID ON PART 1. HOW TO GET 26/5 AT THE FIRST TABLE
EXPLAIN HOW TO GET 26/5 PLEASEEEEEEEEEEE
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.
I WISH YOU SEE IT
can the RHS column be negative values at the end? maybe the solution will become negative for one(or more) variables?
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. :)
Thank you:) So clear and helpful
very nice video
What program and equipment are you using to make this video? I Want to use it for note taking in class. :D
Why can't other authors make simplex this simple?
3:12 i dont really get, why they are non basic?
thank you for your video.... you've made this very easy.
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.
There is an error in 1st video, Row3, column X3 says -2 instead of -7
So are the variables entering and leaving the basis irrelevant?
Would you please do a big M method video tutorial? Please and thank you!
dude the explanation for the new matrix is not there i am lost
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. :)
Can someone tell me how to use calculator to perform these row operations?
I have absolutely no idea how you got 8,0,0 from that last table lol
Thanks for asking! There are three variables here: x1, x2, and x3. x1 is what's called a basic variable and x2, x3 and non-basic. Non-basic variables are set to 0, that's why x2 = 0 and x3 = 0. x1 is basic and it's value is found in the right most column in the row where the basic variable has a non-zero value. In this case, x1 is in column one and row 2 is the only non-zero value in that column, so look in row 2 at the last column to see the value of 8. This tells us x1 = 8. Hope this helps!
@@scottrelliott oof
3:03 I can sense the excitement haha ;)
Thanx very much for telling what is unit column...
thank u ...very nice video
Super helpful. Thanks for the tutorial.
@fastjunkie831 sorry i was wrong :P it's good
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?
What if my two ratios are the same? Which one do I choose to pivot?
if i pass my math b/c of these videos, i'm sending u a check
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.
YOU ARE AMAZING. NOTHING SHORT IF IT.
I m sorted now...thanku for such an easy explanation...
why 26/5 is divided by 2/5...????
Thank u very much.......gr8 works
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.
Great video .. Thank you so much !!
Understood the problem in no time !!
Btw, in my previous comment, I forgot to thank you for the nice explanation. :)
Awesome, thank you. My text-book over-complicated this with many seemingly irrelevant information. It's basically just more specific row operations!
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.
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?
+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
great explanation. you are perfect. thanks for the video
Thank you for the videos! It helped a lot.
thankyou for giving me 20 marks in MBA
Thanks a lot for your help.
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!
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.
Scott can you help us clarify this? please?
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
how to do matrix and pivoting by hand ?
thank you! So very helpful. I have a quiz tomorrow and I actually feel confident because of this.