OMG I am doing MS in the USA and I couldn't understand a lecturer explanation in the USA university but I followed better here, thanks a lot. You deserve to be a professor at a Top university..!!
Thank you very much, Arjun S, for such nice words... it gives a good feeling of satisfaction of doing something useful and at least some of the the concerned people know it and also recognize it... thanks again... :) :)
Thanks Prashant Puaar, i really understood and benefited from your basic way how you explained the dual problems, i am postgraduate student at university of Juba, South Sudan school of management sciences.
Thank you for the video. It was extremely helpful. But there is one mistake in the video. When you separated the equality constraint to two unequal constraints, and changed the sign as it is a minimization, you wrote it as "less than or equal to" instead of "greater than or equal to".
Yes, you are right. I too had observed that mistake immediately after uploading this lecture, but since in the further steps I have not continued to make the same mistake of writing a wrong sign, and, hence, there is no effect of that mistake in the remaining part of the solution, I have kept this lecture as it is. Thanks for watching it carefully and for the comment also... :)
The way of your teaching is very simple and clear at first instance. Thank you for such great efforts as it helps millions of students who want to learn and grow. Best Regards
Thank you for the NICE words! Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
Thank you for the NICE words! Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
Thanks for the video! Good example. Question: Should you have y1 and y4 >=0 instead of y1 and y3 >=0 in your final solution? Want to confirm. Thank you.
thank you sir for your efforts on uploading these lectures. It has been of immense help. It has also helped me in understanding the concepts easily and quickly.
Hello! thank you for the video... Just wanted to point out that in the final step, you mentioned that y1 and y3 are greater than or equal to zero and y' is unrestricted. Did you mean to say y1 and y4 should be greater than or equal to zero? Once again thank you very much for your help
Hi, unrestricted means the variable can take negative or zero or positive value. But, to solve any LPP, by applying Simplex Method or to construct a dual of it, the variable should be non-negative. Hence, we have to substitute such unrestricted variable by the difference of two new non-negative variables.
Prashant Puaar 1 second ago Yes, it may have (-)/0/(+) value... Remember generally there is non-negativity constraint but such variables may have negative value also...:)
The solution is wrong .. When you divided the equality into inequalities you changed the sign from = , (4:19) not only that .. You also multiplied both side by -1 changing the whole problem . So final output (11:02) has -sign multiplied at each constraint row's 1st element which is not right. Even using direct method ..The ans should be .. max z *=160y1+30y'+10y4 sub to contraints ----> 2y1+y'+y4
First of all thank you for watching the lecture with so much interest... Secondly, the solution is not at all wrong. But, there is a mistake of sign in your solution. In the second constraint it should be -4y1 and not 4y1. If you have watched this carefully, you must have found that the objective function and the inequalities in the final dual written by me are correct and you too have repeated them in your final answer by direct method just with an erro of sign in your second constraint. In the name of errors or mistakes there are two minor things in this video: (1) At 2:31, I wrote sign '=', after multiplying by -1, that is actually only a writing error. As far as the multiplication with -1 is concerned, it is unavoidably necessary to have '>=' in both these new inequalities taking the place of the equality. So, there is nothing wrong in multiplying both the sides with -1 after splitting the equality into two inequalities, actually it is necessary also in the case where the sign of inequality in the primal doesn't match with the objective of the problem which you can see in the first constraint in this problem. Hence, it necessary to multiply the first constraint by -1. (2) At the end, i.e. at 10:31, I wrote y3 instead of y4, that is a writing error. If you carefully watch, you can come to know that I have not written y3 anywhere in the final dual whether it is the objective function or the inequalities. y3 only appears in the non-negativity constraint in the place of y4. Thank you... I hope you have got the point. Be more careful at the time of studying.
Thank you so much for the reply. Yes you are right. I did a slight mistake during solving the problem while watching the video , later i realized it but wasn't able to reply due to network issues. Your videos series makes life much easier , I recommended these series to some of my friends too. :) Hope they like the way i do.
Sir please explain how the unrestricted variable in the sign looks like eg. restricted looks like{ >=} . I am unclear on the restricted and unrestricted rule despite checking your first video on rules of duality. And how will we know which variable in the dual is restricted or unrestricted if there is an euality in the primal and that whether the dual is final or not. thank you sir you explain really well.
Unrestricted variable means 'the variable which can take positive, negative or zero value without any restriction, when the LPP is solved'. There is no sign to recognize the unrestricted variable from the constraints, as any variable can take positive or negative value in any constraints by virtue of the real life situation. But it is decided on the basis of the real life characteristic of the variable that whether it can take positive or negative value naturally (e.g. temperature, return on capital, loss in any business or transaction etc are such variables which can take negative value naturally) and on the other hand "non-negativity" is one of the basic conditions of LPP. So, it is necessary to indicate such variables specifically, in the primal itself, as 'UNRESTRICTED" and it is the role of those who first formulate the LPP from the real life situation. For beginners it is necessary to note that the variables which are not recognized as unrestricted can take only positive or zero value on solving the LPP and, hence, they are shown as >=. And also remember that in any LPP there is/are unrestricted variable(s) only if it has been specifically stated in the problem...
sir, as per the duality condition , all the decision variables should be non negative but in this case at the end the final dual form has Y' as unrestricted variable so the non negative condition is not met then. Correct me if I am wrong, as one condition of euality in sign is met but then "all the decision variables should be non negative" is voilated. Please explain Sir.
It seems that you have missed something. If there is an 'unrestricted variable' in the primal, there will be equality in the dual at the same place, and if there is an 'equality' in the primal, there will be an unrestricted variable in the dual at the same place. Thus, it is not necessary that the dual will have only non-negative variables. I suggest you to go through the first lecture and the lectures on 'equality' in primal and 'unrestricted variable' in primal again...
The topic here discussed is the duality in Linear Programming only. Duality in case of Non-linear Programming need to discuss the whole concept of non-linear programming first. I have no plan of covering that topic in the very near future, as there are too many basic concepts to be discussed first here on this platform...:)
Please go to the playlist on "Duality" on my channel, as there is a case discussed in detail on the solution of a primal by solving its dual... there are playlists on many other topics also...:)
OMG I am doing MS in the USA and I couldn't understand a lecturer explanation in the USA university but I followed better here, thanks a lot. You deserve to be a professor at a Top university..!!
Thank you very much, Arjun S, for such nice words... it gives a good feeling of satisfaction of doing something useful and at least some of the the concerned people know it and also recognize it... thanks again... :) :)
Thanks Prashant Puaar, i really understood and benefited from your basic way how you explained the dual problems, i am postgraduate student at university of Juba, South Sudan school of management sciences.
very quickly and effortlessly explained.very good explanation
Glad it helped! Don't forget to subscribe my channel and please also recommend it to the others...
Thank you for the video. It was extremely helpful. But there is one mistake in the video. When you separated the equality constraint to two unequal constraints, and changed the sign as it is a minimization, you wrote it as "less than or equal to" instead of "greater than or equal to".
Yes, you are right. I too had observed that mistake immediately after uploading this lecture, but since in the further steps I have not continued to make the same mistake of writing a wrong sign, and, hence, there is no effect of that mistake in the remaining part of the solution, I have kept this lecture as it is. Thanks for watching it carefully and for the comment also... :)
The way of your teaching is very simple and clear at first instance. Thank you for such great efforts as it helps millions of students who want to learn and grow.
Best Regards
Thank you for the NICE words! Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
Thank you for the NICE words! Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
The best lecture on duality in UA-cam. :)
Your lecture series on Duality is really helpful. Thank You !
Thank u sir....i had a doubt on this particular topic....but after watching your video i clear my doubt.... thanks again
Glad to hear that... keep watching and learning... don't forget to recommend my channel to others... :)
Dil khush kr diya sir😁
Chaa gye guru
Thanks for the video! Good example. Question: Should you have y1 and y4 >=0 instead of y1 and y3 >=0 in your final solution? Want to confirm. Thank you.
thank you sir for your efforts on uploading these lectures. It has been of immense help. It has also helped me in understanding the concepts easily and quickly.
thank u so much sir 🙏🙏🙏🙏 unbelievable way of teaching ...i was confused in this topic ...u saved me .thanks a lot sir
Thanks and welcome
Great lecture. Though I want to mention there is a typo. x1 - x2 = -30
Thank you sir, I really appreciate your efforts which are very helpful for proper understanding of the concept.
Thanks sir it's very helpful
Practical as well as theory point of view
Beautiful. Thank you.
02:23 did you mean to say greater than our equal to?
thank you sir... very clearly your explanation.
Hello! thank you for the video... Just wanted to point out that in the final step, you mentioned that y1 and y3 are greater than or equal to zero and y' is unrestricted. Did you mean to say y1 and y4 should be greater than or equal to zero? Once again thank you very much for your help
Hi, unrestricted means the variable can take negative or zero or positive value. But, to solve any LPP, by applying Simplex Method or to construct a dual of it, the variable should be non-negative. Hence, we have to substitute such unrestricted variable by the difference of two new non-negative variables.
Awesome lecture sir :)
thank you very much sir. this video was very helpful 🙏
Wonderful video Sir. But what is the indicative meaning for word "unrestricted" is. Does it mean it can take negative values also? Plz clarify.
Prashant Puaar 1 second ago
Yes, it may have (-)/0/(+) value... Remember generally there is non-negativity constraint but such variables may have negative value also...:)
@@PUAARAcademy thank you sir.
good video sir
Thank uuuu Mr.... It was good
The solution is wrong .. When you divided the equality into inequalities you changed the sign from = , (4:19) not only that .. You also multiplied both side by -1 changing the whole problem . So final output (11:02) has -sign multiplied at each constraint row's 1st element which is not right. Even using direct method ..The ans should be ..
max z *=160y1+30y'+10y4
sub to contraints ---->
2y1+y'+y4
First of all thank you for watching the lecture with so much interest...
Secondly, the solution is not at all wrong. But, there is a mistake of sign in your solution. In the second constraint it should be -4y1 and not 4y1.
If you have watched this carefully, you must have found that the objective function and the inequalities in the final dual written by me are correct and you too have repeated them in your final answer by direct method just with an erro of sign in your second constraint.
In the name of errors or mistakes there are two minor things in this video:
(1) At 2:31, I wrote sign '=', after multiplying by -1, that is actually only a writing error.
As far as the multiplication with -1 is concerned, it is unavoidably necessary to have '>=' in both these new inequalities taking the place of the equality. So, there is nothing wrong in multiplying both the sides with -1 after splitting the equality into two inequalities, actually it is necessary also in the case where the sign of inequality in the primal doesn't match with the objective of the problem which you can see in the first constraint in this problem. Hence, it necessary to multiply the first constraint by -1.
(2) At the end, i.e. at 10:31, I wrote y3 instead of y4, that is a writing error. If you carefully watch, you can come to know that I have not written y3 anywhere in the final dual whether it is the objective function or the inequalities. y3 only appears in the non-negativity constraint in the place of y4.
Thank you... I hope you have got the point. Be more careful at the time of studying.
Thank you so much for the reply. Yes you are right. I did a slight mistake during solving the problem while watching the video , later i realized it but wasn't able to reply due to network issues. Your videos series makes life much easier , I recommended these series to some of my friends too. :) Hope they like the way i do.
Thank you sir. In the final answer, is it y1 and y3 ≥ 0 or y1 and y4 ≥ 0 ?
It should y1 and y4 ≥ 0 because we have substituted (y2 - y3) by y'... :)
Sir please explain how the unrestricted variable in the sign looks like eg. restricted looks like{ >=} . I am unclear on the restricted and unrestricted rule despite checking your first video on rules of duality. And how will we know which variable in the dual is restricted or unrestricted if there is an euality in the primal and that whether the dual is final or not. thank you sir you explain really well.
Unrestricted variable means 'the variable which can take positive, negative or zero value without any restriction, when the LPP is solved'. There is no sign to recognize the unrestricted variable from the constraints, as any variable can take positive or negative value in any constraints by virtue of the real life situation. But it is decided on the basis of the real life characteristic of the variable that whether it can take positive or negative value naturally (e.g. temperature, return on capital, loss in any business or transaction etc are such variables which can take negative value naturally) and on the other hand "non-negativity" is one of the basic conditions of LPP. So, it is necessary to indicate such variables specifically, in the primal itself, as 'UNRESTRICTED" and it is the role of those who first formulate the LPP from the real life situation. For beginners it is necessary to note that the variables which are not recognized as unrestricted can take only positive or zero value on solving the LPP and, hence, they are shown as >=. And also remember that in any LPP there is/are unrestricted variable(s) only if it has been specifically stated in the problem...
Thanks
Please give me your Divine blessings
sir, as per the duality condition , all the decision variables should be non negative but in this case at the end the final dual form has Y' as unrestricted variable so the non negative condition is not met then. Correct me if I am wrong, as one condition of euality in sign is met but then "all the decision variables should be non negative" is voilated. Please explain Sir.
It seems that you have missed something. If there is an 'unrestricted variable' in the primal, there will be equality in the dual at the same place, and if there is an 'equality' in the primal, there will be an unrestricted variable in the dual at the same place. Thus, it is not necessary that the dual will have only non-negative variables. I suggest you to go through the first lecture and the lectures on 'equality' in primal and 'unrestricted variable' in primal again...
thanks so much sir
Now we can solve this using simplex procedure?
Yes, of course. You'll also find a solved example in the playlist "Duality"
equation that you write at a time 2:20 ..........multiplying constraint with -1 doesn't change =....???
u save my exam
Glad to hear! Keep watching, keep learning! Keep recommending, keep sharing!
thaank u sir
towards the end, it should be y1 and y4 >=0 and not y1 and y3>=0. let me know if m wrong.
u r right ..i also point tht out
can we write the dual of the primal if the primal is subjected to non linear constraints?
The topic here discussed is the duality in Linear Programming only. Duality in case of Non-linear Programming need to discuss the whole concept of non-linear programming first. I have no plan of covering that topic in the very near future, as there are too many basic concepts to be discussed first here on this platform...:)
ok thanks
Sir plz explain me ..how to solve lpp by revised simplex method....😍
sir, plz tell me that how can we find the solution of primal by solving its dual ??
Please go to the playlist on "Duality" on my channel, as there is a case discussed in detail on the solution of a primal by solving its dual... there are playlists on many other topics also...:)
+Prashant Puaar thank you sir
Tq ,sir
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thanks god