Simplex Method - Standard Maximization Problem (free app in description)
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- Опубліковано 7 лют 2025
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In this video we use the simplex method to solve a standard max problem for a system of linear inequalities.
Check out my new Simplex Method app for iPhone and iPads. The link is in the description.
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@Korbyn Xander yea, I've been using InstaFlixxer for since november myself :)
8 years after publishing, still helping out people. Thank you Brian.
3 years after publishing, still helping out people. Thank you Brian.
Dude you are the best. My professor explained it in lecture and it flew over my head. The way you did it is so easy. Now looking back I understand what my prof. said. Thanks!
I agree. My professor knows this, but I just didn't get it. This video explains it so well that I even think it's easy.
Thanks for teaching me in 10min what my professor tried to teach for 10 hours
My online prof taught this with what sounds like a mid 90's Burger King Drive through microphone on a windy day, and the audio only played in one ear, appreciate this bro
I am gonna cry!!Searching for a proper explanation for almost a whole day and finally!!Well explanation!!Finally understood!!You are my life saver!!Thank you!!
Hands on, the most clear and to the point explanation! Thank you for not wasting people's time! :)
So nicely explained. Indian instructors are making so difficult to understand all over youtube for such a simple problem. Thank you Brian making such a useful and easy to understand video.
Thank you so much! I've been struggling with this since several hours but with your explanation I understood it in a couple of minutes. Thanks so much!
I finally leanred simplex only by a simple 12 min video!!! I HAVE STRUGGLED WITH THIS METHOD 3 SEMESTERS NOW!!!!!
+Brian Vietch This is fantastic. I watched other people do this and your version is by far the most clear. Thank you thank you.
+Grant Smith Thanks for the compliment
ONLY video that made me understand simplex method. I tried like 10 videos before.
Great video! It was really helpful. I was struggling with the Simplex Method, and my professor didn't explain it so well. But this video made it so clear! Thanks!
well, i have my final exam in 12 hours, and this will be on it, but i think you have just saved my ass
Thank You. I would love to have teachers like you on school.
Clear & concise. THE BEST tutorial I've seen on Simplex Method. Thank you, you helped a student big time.
A very good explanation of the Simplex Method that i didn't find in any of the books or other references...great job sir..
Need a 7.2 on today's test, you probably helped me out for like 2+ points, thanks mate!
thank you saved my final
bro this my first comment on youtube and I must say that it helped a lot thanks bro !
Thanks a bunch sir , i've literally tried every other tutorials out there ,this was the first one to get me my answer , thanks a lot , i'll sub you !
this is the exact same problem given to me in our homework. thank you so much!!
Thank you for showing us how to use this complicated calculator. ❤
Im really worried about this method. But this video helps me to understand easily. Thank U a LOT
Awesome review! Made it so much simpler and very clear! Thank you for sharing your knowledge. - Engineering Student
Usually. Standard minimization problems are transformed to a standard maximization by using something called a Primal/Dual Table. I don't have a video on that, but if you search youtube for 'simplex method standard minimization,' the first video by Scott Elliot looks promising. He also has a non-standard minimization video.
i just want to know why the Z column is called the junk column ? besides your explanation was by far clearer although i did not understand how you could tell if the columns were basic.
Basic columns are 'unit' columns. Unit columns are columns that can be written with a 1 and the rest 0s. So (1,0,0) or (0, 1, 0 , 0) or (0, 0, 1, 0, 0).
Excellent explanation. The best I have seen, Bravo.
Thanks you saved my ass on my upcoming math final
Great explanation, probably one of the best vids explaining it. But I think I'll just stick to coordinate graphing.... lol
you teach better than my Econ lecture
Thank you so much for your step-by-step video. Soooo easy to follow...
Thank you so much!!its the only video that helped me solve the second table!!!!!
Even though we are trying to row reduce, the element we pivot around in the Simplex Method matters. Because 90 is the smallest ratio, we need to pivot around that row. That's why we pivot around the '2'. You can still switch rows. It just won't change the element you pivot around.
best explantation ever! Thank you so much
hi brian thank u so much first of all even though only in the middle of the video but seems a lot clearer can you just explain why u have multiplied the first row by 0.5? why did you choose a half?
+Simon Bentley The first element in the first row is my pivot element. The most straightforward way of starting the row operation process is to make the pivot element into a "1". Since the number is a "2", I multiplied the row by 1/2. This turns the 2 into a "1". You can also divide the row by 2 (but that's basically doing the same thing).
Basic columns are just columns with a '1' and the rest '0's. It just turns out that the 'w' column ends up being a basic column. Back when we introduced the slack variables, it just means 'w' was needed in order to get the equal sign.
Best explanation for me so far, thanks
You are my man. This was just the right video for my project
it's best I have seen about simplex lecture! great
Thanks a lot Brian!!Very much informative...I wanted to know whether any video for minimization problem too.. do we need to convert a minimization problem to a max problem to solve it?
oh my gosh thank you! the video was insanely helpful
The solution is x = 48, y = 84, and z = 0. If you let z = 60, it won't satisfy the initial inequalities. When you're done with the simplex algorithm, you read off the table like w was a basic variable. w = 60 doesn't really mean anything directly. z = 0 means the z-variable wasn't actually needed to give an optimal solution. If you think of how solutions are interpreted geometrically, the corner where the system is optimized occurred on the z-plane (z = 0). So z is like a junk variable now.
bro you are awsum . been trying to figure it out from the books and they used so much of ki fi and pi terms to confuse the hell out of me ....
Geezzz thank you so much bro! You really save me from my reporting about simplex method in lpp thank you so much!..
I have a question. Do slack variables have a meaning? Except helping us solve it of course.
Amazing explanation by the way.
My explanation may not be amazing but I'll give it a try. Remember when you solved systems of equations? Like 2x+y=10 and x-y=4? The answer was the intersection of the two lines.
With systems of linear inequalities the answer is not an intersection but an entire shaded region. But when adding the objective function, i.e., Maximize P=2x+4y, the answer must now be at a corner (i.e, intersection of two lines) of the shaded region.
We can't use augmented matrices until we have equal signs. We introduce the slack variables so that both sides now balance to give us an equals. For example, 2+5
Brian Veitch I understand the concept of slack variables. I'm not sure I completely understand what you're writing since English isn't my native language but I wondered if these variables have a meaning like the explanation of "λ" in langrange optimization.
thanks for the answer anyway.
Honestly they just represent the resources in the LP problem that are not used. I'm sure there is a much more technical answer but none that have helped me understand them more. The theory can get really abstract when you venture into the high level graduate courses. But for lower level undergraduate math classes (where this is usually introduced) they are used so we can use an augmented matrix and to keep track of how much of a variable we do or do not need.
I'm sorry I couldn't help more.
To find the maximum, don't you pick the largest value from the objective function and the largest from the divided rows too?
Thank you: very well done. Great effort and nice pedagogical style.
Work of Art! Great solution.
Thank you.
Thank you very much you're a legend mate!!
Hi, at 4:30 you used row operations to turn the numbers of the last 3 rows in the first column into zeroes. Why'd you do that? And what if my pivot is in the middle, e.g.: column 2, row 2.
+lynx821 It's like row reducing with matrices. Whatever is your pivot element, you turn it into a 1 and the rest of the numbers in that column to 0s. In your example if we pivot around column 2, row 2 then you turn the 3 into a 1 and the 1/2, 1, and -5 into 0s.
+Brian Veitch All right, thanks a lot man! Saved me a lot of time and my mid years.
Just cracked the code thanks to this video. Been looking for someone to explain it right for hours. Thank you!!
thanks a lot, what software do you use? the board and calculator?
Hey, what if you do the ratio test and you have a negative number, what do you do then?
how did you determine which variables are basic and which are not? And, you never seem to bother with entering variable or leaving variable, therefore, how did you properly interpret the final table??
Hello thank you for clear explanation can I use this method for minimization problem ?
You can't use this technique right away. For a standard minimization problem you need to set up a dual table. This eventually leads you to a new system of inequalities. Then you can use this technique. Reading the final answer from the table is also different. I have a flow chart in the video description to help guide you through the process. I recommend ua-cam.com/video/BdtdYlUIXak/v-deo.html. This video lays out the process pretty well.
@@BrianVeitch Thank you very much 🤗🌹
P=0.16x+ 0.14y
x+y
I didn't quite understand why the concept of the Basic and Non-basic columns. Why is Z for example an Non-Basic column? Great Video!
Kind Regards
Philippe De Soure Think of it like row reducing a matrix. You want to get your columns so that they have a 1 and the rest 0s. For the simplex method, they just call this a Basic Column. Non-Basic columns (or commonly called junk columns) don't have this form and tell you that the variable was not needed (i.e, z = 0). Honestly, I haven't looked into the how and why this method works.
Thanks Brian.. I did watch the one by Scott and solved it.
How can you decide which one is basic column and which one is junk?
great video. Can i know what app u use for explaining this? Would love to know it.
I'm using camtasia for filming and smoothdraw to draw.
Thanks for this, now i alreday understand what is max.
Thank you very much. it was very helpful to me :)
thanks a lot!! you have a very nice way of explaining the concept :)
5:51
Guys, which mode on the calculator CASIO must I choose in order to perform such calculations?
even i want to know..please tell
I'm not sure what you mean by mode. Are you talking about how I do the row operations in my calculator?
i m using casio fx-991ES PLUS ..so how to do row operation in that model?
I have an idea but I need to get my hands on that calculator. There are a lot of different versions of a casio fx scientific calculator. I teach a lecture of 120 students today and maybe one of them has one for me to look at.
please check..that would be a great help to me..thabkyou
What does it mean to have 60 of slack variable of W ?
It means the equation associated with that inequality was not satisfied. It makes more sense when it comes from a word problem. Say for example you want to sell three types of chairs. Chair A takes 1.25 hour, B takes 2 hours, and C takes 3 hours. With an 8 hour workday, this gives us the total hours spent in one day as
1.25x + 2y + 3z
@@BrianVeitch thank you so much !
ahhh i looked down and found the answer already :D Thanks muchly for this incredible video
Very helpful, thanks.
I don’t understand where the 0’s come from why it’s 0 0 then a random 1??? In the simplex table?
Thanks for wonderful explanation but why z is not basic column but w is basic?
w is basic because the w column is a unit column (one 1 and the rest 0s).
Brian Veitch thanx
sorry how to decide which is column is basic or nonbasic? and thank you so much!
if a column has all zeros except 1 one, that would be basic
Amazing video, it's really good.
What happens in the step of dividing my "C" column by my pivot column if my "C" value is 0? My result of the division is going to be 0, so do I consider it when comparing with other results, or I just ignore it?
You can ignore it. You need the one with the smallest Positive ratio.
Thank you so much for the video!
Hi, i've got a question for 1st pivoting step. What's going un with all row if x in 2nd or 3rd equation is equal 0? We are leaving all row without any changes ? Thank You for an anwser.
+Majkel matka teresa I'm not sure what you mean.
how do we find pivot row when the C column has, for example, two 0 entries? Would you use the first zero row as the smallest?
If it does and all the constant values are 0 then you may not have a feasible region (no answer). Or the Simplex Method won't work with the contraints you've given. I've never seen it happen so I'm curious if you've come across this.
How do you separate basic columns and junk columns?
hello there, how did you re write the objective function? how did it all turn to negatives?
Please help me. Thank you
@Brian Veitch I understand that basic columns are those, where in objective function row is 0 (so x, y and w maches that rule) but what about P? It has 1 in objective function row. Is P an exception from that rule? Maybe there is another rule for that? Or is it always considered as a basic column?
Thanks in advance for Your help.
Bartosz A. It’s not that there’s a 0 in the objective function row. It’s that the column is a unit column (a column with a single 1 and the rest 0s). So the P column satisfies that rule.
@@BrianVeitch Ah, i see now. Thank You!
At 8.05, shouldn't it be 120 rather than 240?
At roughly 3:16 can we not switch the second row with the first??
So I assume if looking for min, then you would be looking for, in the first Simplex Table, the largest one (while you looked for the most negaive, i.e. the smallest)??
+DarthAlphaTheGreat largest "negative" is the smallest number ultimately.
what model and brand is the calculator ??? please someone respond me
❤️... I love the application
where do you get that awesome calculator, Sir?
Sir while changing the 1st row( when we multiply R1 with 1/2), won't we change 90 to 45 as 1/2 is being multiplied to complete row?
There isn't any place where you need to multiply 90 by 1/2. Around 2:40 I had to multiply 180 by 1/2 to get 90. There's also another place later in the video where I had to divide 90 by 1/2.
I got it, Thank you! :)
what happens if we get same values wen dividing C column with pivot column..
like your initial C column was 600 ,300, 1000?
please reply fast..
If you get the same ratio then you should be able to choose either one.
+Brian Veitch ,thnx ..this is a really gud method..
Very helpful, thank you so much!
What Happens if the second pivot element is in the same row as the first pivot element? This would mean that the 1 in the first column would change as the second pivot element becomes a 1.
Avinand Rampersaud That's a good question. I don't know the answer to that. I suppose if it happens then you just keep working the table as usual.
can i do the row operations @5:31 on standard scientific calculators??
Of course. You can use any calculator that can deal with fractions. You can do one number in each row at a time instead of the entire row at once. I just did this way to speed up the calculations.
Do you have to use the row in which the Pivot element is in in each step of the row operations? Or could you do, say, R_3 - 2R_2 --> R_3?
Sarah Shackelford For your example of R3 - 2R2 -> R3, this means to me that R2 is the pivot row. If R2 is not the pivot row I'm not sure if that operation will do anything for you.
The row with the pivot element is the pivot row. You should use the pivot row in each of the row operations for one "cycle." For example, suppose R2 is the pivot row. You must do a row operation with R1, R3, and R4 using R2 as the pivot row. Once you're done with R1, R2, and R4, you can start again by choosing a new pivot element and pivot row. But make sure that your operations always use the pivot row. Hope this answered your question.
Brian Veitch Thank you, Brian. Just curious...do you know why that is? I know that if I don't use the pivot row, I get a different answer...but I can't figure out why that would matter.
Sarah Shackelford math.stackexchange.com/questions/39306/simplex-method-row-operations-help. Skip about halfway down to the answer that starts with "I'll assume you are using a nice full table that ..." This person's answer is quite long but about halfway through the answer he or she goes through an example explaining what would happen if you choose an operation that didn't use the pivot row. His or her conclusion is that after each cycle of row operations, you must always have the identity matrix hidden in there somewhere. So for my example, there is always a column with (1,0,0,0), (0,1, 0, 0), (0, 0, 1, 0), and (0, 0, 0, 1). Doing a row operation that doesn't use the pivot will probably leave you with a table that loses one of these columns. Doing so means you won't be able to read the answer correctly.
Brian Veitch That makes sense. Thank you!
if we have a min problem we have to take -max ...but in the table the objective function willl be with positive sign???
+Penny Gr Is it a min problem where the contraints are less than signs or greater than signs? If they're less than signs then do the problem example like a standard max (just negate the final answer). That is if your final answer is P = 20, then your minimum is C = -20. The objective function will still start as negative in the table.
If the contraints are greater than signs, then you have to do a method using a dual/primal table. The setup takes some time and you'll need a different video for that.
+Brian Veitch thank u for the answer..also do you have a video for simplex two phase???
Thanks a lot, Brian! :)
If a slack variable becomes a negative in the bottom, do I then have to optimize the slack variable?
I'm not quite clear what you mean by negative in the bottom. If it's a standard maximization problem and you follow the procedure, I don't think that will happen. If it does, my guess is you weren't suppose to use a standard max setup.
If a slack variable remains non negative after the last row is positive, you got your max (708 here) correct. The thing that changes is that this max is achieved by not using fully the resourses you have. I dont know if i helped, just needed to point that about slack vars.
Why was the last column taken as a basic column?
thank you a lot. It helps a lottttt!\
+Brian
Hi Brian I did a question and got this matrix.....
1 1.2 0.2 0 0 2
0 4.4 -0.6 1 0 10
0 6.8 1.8 0 1 18
How do I know what my shadow prices and reduced costs are? What's the rule for each problem I come across?
What was the original problem?
thanks,,,, I have solved my homework recently :D