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May 20, 2015 at 7:39 am
May 13, 2015 at 7:39 am
Thank u john
May 12, 2015 at 6:55 pm
This is probably a silly question, I’m possibly missing something … but why do we need to do the graph? Why can we not just use the equations to determine the optimum solution?
John Moffat says
May 12, 2015 at 8:06 pm
No you can’t (and I do explain why not in the lecture).
If there are three (or more) constraints, then solving the equations for 2 of them at a time will not tell you whether or not they are inside or outside the other constraints.
In addition, the examiner specifically tests you on whether or not you understand the graph – sometimes you have been asked to draw the graph, and on other occasions you have been given the graph. In either case, simply solving equations would not be doing what was required.
May 12, 2015 at 8:12 pm
Oh I see, thank you. And my apologies for asking something you answered in the lecture. So much information to try and retain!
March 28, 2015 at 1:31 pm
If there is spare capacity/slack for materials or labour, than is the shadow price 0 as well?
March 28, 2015 at 1:49 pm
Yes it is.
March 28, 2015 at 2:05 pm
Thanks for the promt reply as always.
I wish theres spare capacity for everything, saves a lot of time
March 23, 2015 at 1:02 pm
Hi, I have a question. I never really concentrated on this, until I met the way you did the programming. I usually put x and y as variables and graph them correspondingly (x axis and y axis). This time I put S and E as you have done and put S on x axis and E on Y axis and got totally different graph from the one you got. What is the right way to go.? I know this question may seem primitive, but I decided to ask. Thanks in advance.
March 23, 2015 at 1:06 pm
It does not matter which axis you use for which variable. The graph will look different (sort of sideways ) but provided you label everything properly it gets the marks whichever way round
March 23, 2015 at 1:08 pm
You simply motivate me to study. Thanks a lot.
March 2, 2015 at 3:20 pm
Thank you mr. John I am really happy to get you lecture and excited for next exam. I will definitely clear this time. ????
February 23, 2015 at 5:15 pm
I just don;t get it all I am spending hours on it and can’t get it right
February 22, 2015 at 10:30 am
Sir, in the lectures, you said that maximum contribution is at point B which is correct and same was also proven when you have calculated the max cont at point A. But Sir my question is, “in the graph, on what basis you have said that B is the best point”. Because if i am not mistaken, in the lecture, you firstly said that B is the best point and then you have calculated the max cont and then you have shown the difference in contribution between point A and B.
Thank you for your help Sir.
February 22, 2015 at 10:33 am
B was the best point because when I moved out the contribution line (keeping it parallel), B was the furthest point away from the origin.
February 22, 2015 at 9:26 am
Sir, thank you for the fabulous lectures, it really helps.
However i am confuse about one thing. In the Question 1, the requirement is firstly ‘Find the optimal production plan’ does the answer is the feasible region drawn in the graph.
In addition, kindly advise why do we calculate ISO contribution? Why must we draw the ISO contribution line in the graph.
Thanks to help Sir.
February 22, 2015 at 9:46 am
The feasible region identifies which combinations of the two products satisfy the constraints.
We need the contribution line to find out which of these combinations is the optimal (i.e. gives greatest contribution). We move the line as far away from the original as possible and the optimum is the corner of the feasible region furthest away.
February 21, 2015 at 3:07 pm
thats a very good lecture sir my question is what is mean by iso contribution line
February 21, 2015 at 3:14 pm
‘iso’ means ‘same’. So it is the contribution line that I draw in the lecture.
February 5, 2015 at 9:48 am
I am so impressed and satisfied with Open Tuition. Thanks a million, I never understood limiting factors as much as I do now. Thanks
November 24, 2014 at 7:52 pm
6s+9E= $ 225 (S=0 ; E= 25) ( E=0 ; S= 37.5)
since Contribution comes out of to be $225, if we check the the contribution if it is out of the red shaded bodx or not it is actually is, i did not get it is..
December 30, 2014 at 4:21 pm
yeh thats true….you’ve confused me aswell now lol
December 30, 2014 at 5:08 pm
It is not a question of whether or not the contribution is inside or outside the box!! That does not make sense.
The optimum mix is at point b – the point furthest away from the origin. This point is on the edge of the feasible region.
When we know what the values are at that point then we can calculate the contribution.
The values stated by Imran for S and E were purely for being able to draw the contribution line – there is no other relevance of them.
November 4, 2014 at 12:04 am
Great video! Thank you! checking out the next video now.
August 30, 2014 at 8:59 am
The example you’ve shown here is a 3rd example, which I encounter since I study F5, where the highest profit is earned at the intersection of labour hours and machine hours lines. Is this a rule? If yes, why don’t we go straight to that intersection?
Why did you say that that the any of the corners could be most profitable?
August 30, 2014 at 9:34 am
No it isn’t a rule. The highest contribution will be earned at whichever of the corners is the furthest away from the origin when moving out the iso-contribution line.
If you watch the video again you will see that if the line were a different angle, then when it is moved out then a different corner could be the furthest away.
If you are not sure what I mean, just suppose the question was exactly the same except that the contribution per unit for S was $10, and for E was $1. The constraints are all the same and so the graph is the same.
However, point A would then give the highest contribution ($360). Point B would only give a contribution of $305.
August 21, 2014 at 9:02 am
Waw!Thank you sir!Exceptional lecture!Very well done!
July 2, 2014 at 3:49 pm
thanks a lot it is of value and explicit.
Mpazi Siame says
July 1, 2014 at 3:02 pm
Great lectures plz make these videos downloadable. Thank you
July 1, 2014 at 3:05 pm
Sorry, but no – we will not make them downloadable.
It is the only way that we can keep this website free of charge.
You can download the Course Notes, but the lectures can only be watched online.
July 1, 2014 at 3:56 pm
Alright this still good staff sir. Thank you onceagain
May 19, 2014 at 1:53 pm
Very good lecture – Thanks that made it alot clearer
May 17, 2014 at 8:14 am
Great Lecture sir!!! Understood it very well
May 8, 2014 at 7:57 pm
I take it there is no rule at all for deciding which axis to put which product on?
Thanks and best regards
May 9, 2014 at 5:10 am
That’s true – it doesn’t matter which axis you use for each product.
May 7, 2014 at 2:53 pm
Hiii sir, your lectures juz awesome 😀
I have a question… Will be my answer considered wrong if thers a diffrnce in my optimal solution,whethr if i use “inspection” or “drawing ISO contribution line”?
May 7, 2014 at 4:09 pm
It depends what you mean by ‘inspection’.
The only alternative to drawing the iso-contribution line is to calculate the total contribution at ever corner of the feasible area.
(But still read the question carefully – obviously if it specifically asks for you to draw the iso-contribution line, then there is no choice )
April 23, 2014 at 8:00 am
Hello sir . Very nice lecture .. Sir i have a question .. That why we made third equation ? And what is its link with point B ? And sir if its all about calculating equations then why we plot graph .. Why we dont do all this in the begining ? Thankyou sir
April 23, 2014 at 8:35 pm
We plot the graph because the exam will require it!
We cannot just solve the equations without the graph because we do not know what the relevant corners of the feasible region will be. As it turns out in this question, the demand for executive chairs is redundant, but we would not know this if we had not drawn the graph.
April 24, 2014 at 5:49 pm
thankyou sir .
April 25, 2014 at 9:38 am
You are welcome
March 10, 2014 at 3:06 pm
Sir, what can be used to draw the graph in the exam; black Biro or Pencil?
March 10, 2014 at 3:12 pm
You can only use black ink in the exam-pencil and other colours are not allowed.
March 9, 2014 at 3:09 pm
Sir I so much appreciate your wonderful lectures. Is it possible that there will come a question on cost minimization in the exam under linear programming?
March 9, 2014 at 3:10 pm
Yes, it is possible.
March 9, 2014 at 3:33 pm
Is it possible to have a lecture on that from opentuition?
March 9, 2014 at 3:44 pm
There is no need for a lecture – really – because the logic is exactly the same.
Although cost minimisation is possible, it is not very likely, and all that is needed is to have a go at one or two from your Revision/Exam Kit.
February 9, 2014 at 8:40 am
Hi sir, I was working a question from my BPP kit on linear programming and there were products A and B. I did the graph but only product A had a demand of 1000 limit. But on my graph I named product B as my X-axis and product A as my Y-axis. Then when I plotted the Demand line, it was a horizontal one instead of vertical(as I used y-axis for A). In the kit, it’s done the opposite way i.e A being x-axis. My question is, is it a fault in the exams?
February 9, 2014 at 9:42 am
It does not matter which way round you have your axes. The graph will look different (because it is sort of sideways ) but the final answer will be the same.
November 21, 2013 at 7:53 pm
I really enjoyed this lecture. Thanks a lot Mr Moffat. I have a question though: Does it matter if Standard or Executive (as in the example) is plotted on the Y axis? Can Executive be on the Y axis also? Thank you.
November 21, 2013 at 7:59 pm
No – it does not matter which axes you use
November 21, 2013 at 8:01 pm
Okay. Thank you very much once again.
October 27, 2013 at 9:50 pm
Just wanted to feed back what a good lecture this is. I was struggling with Linear Programming and this has helped me see things a lot clearer. Fell much better now the penny has dropped!
October 4, 2013 at 6:02 am
Hi! what is the use of graph if we can get reasonable answer by deriving the equations?
October 4, 2013 at 6:55 am
You can calculate where each 2 lines cross, but if there are more than 2 constraints it will not be obvious without the graph which points are not feasible – I mention this in the lecture.
Also, if the question later mentions that one of the constraints changes, then the effect is more obvious if you have the graph.
Finally, the examiner will ask for the graph and therefore if you have not drawn it you will lose marks!
September 28, 2013 at 10:13 am
Hi sir can i just work out the contribution for each line instead of using the ISO method?must I know both method?
September 28, 2013 at 10:21 am
I think you mean the contribution at each corner of the feasible region (because the lines themselves do not have contributions!).
Assuming that is what you mean, then you can do this and then choose the one with the biggest contribution, However, you must write what you are doing (so the marker is clear) – something like ‘because of the theory of iso-contribution line, I have checked all the corners and the best one is…….’
You must still graph the constraints because it will be asked for, and without it you will not know what the feasible region is.
Also, read the question carefully – if it actually asks for the iso-contribution line then obviously you must draw it.
September 2, 2013 at 5:53 pm
Hi Mr. John, I have a doubt in iso contribution area. That whether it is compulsory that our iso contribution line to be remain in the feasible region area or contribution line can be drawn pass the feasible region.
Can you please clear my doubt.
September 2, 2013 at 9:50 pm
The iso-profit line is best drawn within the feasible area. (It can be outside, but it makes it easier to make mistakes and choose the wrong point. Also it means that your constraints will not be filling the graph as much as they could have)
June 4, 2013 at 10:24 am
Thank you Sir John for this. But during the lecture you said you’ll explain later on how the values were derived for the X-AXIS AND Y-AXIS, giving a maximum value of 40. However, the lecture ended but no explanation was given as to how we derive those values? Could you please explain now.
June 4, 2013 at 10:31 am
It does not matter what maximum values the axes go up to.
However to make sure that I get a nice big graph, what I do is decide on the points I want to plot for each of the constraints first. Then I fix the scales on the axes to make sure that they are at (or a little above) the maximum I want to plot for x and the maximum I want to plot for y.
This then makes sure that the constraints will actually fit on the graph, and also that they are nice and big
May 12, 2013 at 7:46 pm
Thank you very much! i appeared for my F2 exam in november 2011, my first attempt of F5 will be dis june, dis was a great revision lecture! now i ‘ll move on to the second lecture! Thank u very much sir!
May 8, 2013 at 8:49 am
Why are we not considering point A? Because A seems to be farthest away from the origin, isnt it? Please reply soon…
May 12, 2013 at 7:53 pm
Its not just choosing the point furthest from the origin – it is a question of getting the contribution line as far as possible from the origin.
Amanah Saeed says
November 14, 2013 at 9:19 pm
at point A, contribution is $ 216, At point C; contribution is $ 210 and at point B; contribution is $ 225. Thats why we picked point B, because at that point the contribution is the highest (max.) – plz correct me if iam mistaken.
November 14, 2013 at 9:39 pm
You can check all the corners by all means, however if you draw the iso-contribution line then you can find out from that which is the best corner and then that is all you need to check.
(Checking all the corners is fine, but you must make sure you understand about the contribution line because you just could be asked about it specifically)
April 25, 2013 at 10:31 am
i wish linear programming comes this june
April 25, 2013 at 6:03 pm
Linear programming will certainly come again soon. I think there is a reasonable chance it will be this June, but that is only a guess – you had better make sure you are happy with everything else as well
April 30, 2013 at 9:03 pm
so John do you think that we may get a graph such as the one on the 2010 paper or we will have to plot the graph
May 1, 2013 at 9:43 am
If it does come up in June then it could be either. In the past you have usually been required to draw the graph yourself – the one in 2010 was unusual in that it gave you the graph.
April 16, 2013 at 6:45 am
Sir John, Thank you so much for all the resources you and your team have been providing via opentuition. I have one quick question. what is the chance of this area being tested at P5 level.
April 16, 2013 at 8:03 am
Linear programming is extremely unlikely to be examined in P5.
April 17, 2013 at 5:41 am
Just as I thought…Thanks a lot!
April 15, 2013 at 11:51 am
I am not able to view the videos. It says that there is a server problem. Can I get some help please. I really need to view these.
April 15, 2013 at 5:12 pm
The videos are working fine – the problem is likely at your end. Try clicking on the ‘technical support’ tab at the top of this page for suggestions.
April 15, 2013 at 5:13 pm
server problem means that you are most likely behind a firewall. contact your internet provider for help
April 11, 2013 at 1:33 pm
good lecture,but i could’t understand that whether ISO CONTRIBUTION line is necessary to draw or not.
April 11, 2013 at 7:56 pm
Yes – you have to draw it for two reasons:
Firstly, if you do not draw it then you do not know which of the corners of the feasible region is the best. It could be any of them. (OK you could check each of the corners separately, but this would waste time).
Secondly the examiner expects to see it and there will be marks for showing it
April 6, 2013 at 8:06 am
Mr John, I just want to say that I am having a course with one of ACCA learning partners who has a golden status “i don’t really want to mention the name” and I didn’t understand a word of linear programming!! As I watched your lecture, I think it is one of the easiest topics where I can score marks and I am really hopping it will appear in June’s exams!
Thank you! and btw this is the case with most of F5 lectures, I have to come here to understand the topic! Thanks!
April 6, 2013 at 8:24 am
Thank you very much
March 22, 2013 at 8:13 am
hello, i have just started using an android device and i cant seem to play the videos. is android not supported?
March 22, 2013 at 8:52 am
Since android out of the box does not support these days flash or mp4
Answer is no
But if you look around android store and download flash player or some browsers many students made it work
March 23, 2013 at 6:35 am
ok, i’ll try to get round it somehow. many thanks
March 28, 2013 at 10:51 am
hi mate ..I had a same roblems as yours .. I got not 2 .. video didnt play but download opera from androi market and it plays any video ..my works fine ..pls do so its lovely apps ..thanks
February 26, 2013 at 7:44 pm
Waal what a great lecture!! this is excellent to say the least, i will definately use open tuition for better results…. thank tutor keep the good work up.
February 5, 2013 at 7:40 pm
thanxxxxx thanxxxxxxxxxxxxxxx alot , we all love u so much Adim,GOD bless u, i wich every body could think like u this world would be like heavn…………….thanx again
January 20, 2013 at 10:39 am
why do we use 40 as max values for X and Y axis ?
January 22, 2013 at 7:36 pm
because Maximum Production of Standard chair is 40.
November 14, 2013 at 9:26 pm
where this is written??
November 14, 2013 at 9:36 pm
It is not written, and it is not true
The reason is that we want a ‘big’ graph that fits nicely on the graph paper. The points we need to plot for each line are a maximum for both x and for y of 40 (or close to 40) so if the have the axes going up to 40 then we will get a nice ‘big’ graph. That is all. It doesn’t really matter what your axes go up to, but if the went up to (say) 500 then you would end up with a tiny little graph which would be no use to anyone.
December 2, 2012 at 11:46 pm
I actually think your lecture is brilliant and its free. I will pay a premium if i have to. Thank you.
March 22, 2013 at 6:27 pm
December 1, 2012 at 12:22 am
John, thank you for the excellent lecture on linear programming, you’ve got Empathy
November 13, 2012 at 1:05 pm
what would be the equation if demand is less than the point where material & labour are intersecting??
October 24, 2012 at 7:29 pm
Very helpful. Thanks alot!
October 22, 2012 at 12:04 pm
Hi Admin..i have question as explain in example that Iso-Contribution line could be anywhere but if it is after the corner B or A then what is it will be right or not. one thing the optimal point will always be where they constraints cross each other. ???? Please reply me
October 8, 2012 at 5:11 pm
Thanks a lot
September 25, 2012 at 11:47 pm
Sir your way of explaining the last equation was soo clear , your method is much easier…… thanks a lot ……
September 5, 2012 at 10:54 am
Very good Lecture I wish I could have listened to him before
September 2, 2012 at 10:46 am
Why cant we play this video on tablets. And in my pc the video stops in d middle ftequently. It says server error smthin like dat.
September 2, 2012 at 9:46 pm
If your tablet plays mp4 files
Videos will work
Try another browser??
There are many tablets – lectures work on most of them
With or without flash
August 20, 2012 at 10:48 am
I believe in a situation where we have an accurate graph then we have to get the answer by reading the graph and not determine the answer by solving the equations. Is that so?
August 20, 2012 at 2:59 pm
@self, In the exam you will always be expected to be able to solve using equations.
However well you draw your graph it will never be as precise reading from the graph as it is solving the equations.
You still need the graph to be able to know which equations to solve.
August 21, 2012 at 3:19 pm
@johnmoffat, Wow…thanx a lot. You brought light into the dark!
August 22, 2012 at 9:22 am
August 7, 2012 at 12:53 pm
dont stop plz, God wl reward you
August 6, 2012 at 12:01 pm
VERY VERY GOOD. PLEASE DON NOT STOP THIS FREE SERVICE. I PROMISE I WILL DONATE WHEN I BE EMPLOYED. GOD BLESS YOU
July 21, 2012 at 11:09 pm
adel mokbel says
June 8, 2012 at 12:57 pm
very prof lecture
June 8, 2012 at 12:37 am
May 30, 2012 at 3:19 pm
good lecture… easy to follow.
May 19, 2012 at 5:37 pm
@admin I can’t see any videos. Should I do anything extra to see them?Thanks
May 19, 2012 at 5:43 pm
try google chrome browser
May 15, 2012 at 5:52 pm
@admin. i have been watching the videos all along until yesterday. and now i have just logged on but all i can see is the comments, there are no vidoes, please help.
March 29, 2012 at 12:08 pm
the lectures is good but i still have a problem with how he got the scales.he didn’t say it later as promised.
March 29, 2012 at 9:12 am
Excellent. Very well explained. Great Lecture. Really enjoyed the lecture!
March 11, 2012 at 7:36 am
wow!I wonder why I did not listen to the lectures before;They are totally effective!
Your lectures are amazing…I love the way you make everything so simple,yet comprehensive.Keep up the good work!!
March 4, 2012 at 9:33 am
March 1, 2012 at 3:41 pm
February 26, 2012 at 4:02 am
The topic was explained really well in a very clear manner. I did not understand this before- now I’m really confident.
February 26, 2012 at 2:38 am
I fully agree- theoretically the whole graph is a waste of time.
March 4, 2012 at 4:12 pm
@malka77, the graph is not a waste of time for two reasons:
One is that the maximum could occur at any of the corners of the feasible region. The only way that you can do it without the graph is solve for when every two constraints cross, and then check which ones of those are not feasible because they break one of the other constraints. (The lecture explains why this is so)
Secondly, the examiner regularly tests you on the graph – either by asking you to draw it, or by giving you the graph in the exam.
March 5, 2012 at 1:08 am
What I meant to say was that there are two methods- either through graph or by using simultaneous equations. Since the graph requires you to use simultaneous equations- is it not better to just study that method? That is why I do not understand why the use of graphs is required as part of the specification.
July 13, 2012 at 11:22 am
@malka77, You still need a graph, because suppose there are three constraints. Each pair of lines crosses at a point and so there are three points you will find using simultaneous equations. However, one of those points could well be outside the feasible region (because of the other constraint). Without having drawn the graph you would not know this. (You could check, but then because of the time taken, you would have been quicker drawing the graph and then only need one simultaneous equation)
February 23, 2012 at 11:25 am
I liked the way you explained. One thing I didnn’t get is why did u take the point B when it has nothing to do at all….I mean the way we took out maximum contribution was a simple mathematical solution…So why take B and run out of time???
February 22, 2012 at 7:34 am
January 27, 2012 at 7:07 am
iam looking for the f5 limiting factor and em confused if this xample is frm f2 book or f5 book??
January 27, 2012 at 9:06 am
it used to be in F2 & F5 syllabus,
Now, it’s only in F5
November 30, 2011 at 10:55 pm
really helpful, thank u
November 14, 2011 at 8:54 am
thanks keep it up
November 4, 2011 at 10:43 am
i’v been missing in action. opentuition is absolutely great! but whats happening to linner programming? its not playing throught.
DA CEILSO says
October 28, 2011 at 12:21 am
this lectures is very very fantastic
October 27, 2011 at 7:54 pm
o wow this is great,well explained,thank you
October 24, 2011 at 3:52 am
Excellent lectures, opentuition is the best!!!
October 19, 2011 at 10:22 pm
August 16, 2011 at 4:04 am
can we solve these equations directly on calculator and putting on the answers directly of equations, is it OK ? ?
August 17, 2011 at 10:31 am
syedazmat, at F5 – i dont think it would be ok as every step would have a mark and most marks are being able to show to the examiner that we know what we are doing..
June 14, 2011 at 10:57 pm
June 5, 2011 at 12:32 am
I heard from kaplan tutor there will be a graph paper given for Jun 2011 exam,does that mean that we shold be perfect in our graph?
June 4, 2011 at 10:57 pm
I heard from kaplan toutur there will be a graph paper given for Jun 2011 exam,does that mean that we shold be perfect in our graph?
May 4, 2011 at 3:43 pm
Isn’t there any other way other than drawing an iso-contribution line, as we don’t always draw an perfect graph and a simple change in the angles could alter the solution?
April 10, 2011 at 6:52 pm
My lecture stopped aprubtly @ 27 mins any help?
March 22, 2011 at 5:01 pm
I have tried but the lecture is not running on my computer as it was running before?
March 15, 2011 at 2:38 pm
superb lectures of f5
March 5, 2011 at 12:02 am
February 4, 2011 at 10:54 pm
The best one thanks.
February 3, 2011 at 5:48 pm
nice work thanks
January 23, 2011 at 10:01 pm
Realy good lecture, thank you
December 8, 2010 at 10:26 pm
can’t believe i finally understand!!!!……
December 6, 2010 at 10:03 pm
I finally got it!!:)
December 5, 2010 at 5:20 am
really like this lecturer!! very neat and clear. thank you so much
November 24, 2010 at 9:12 pm
I would say, It is very good lectures
November 24, 2010 at 12:31 pm
thank you so much
November 18, 2010 at 10:16 pm
Very Helpful. Really good leacturer, easy to listen to and makes point of all the relevant areas. Thanks, i was confused before i listened to this.
November 16, 2010 at 8:39 am
very helpful, thank you
November 13, 2010 at 1:21 pm
A mazing.. very clear and understable lecture. Excellent!
October 25, 2010 at 4:01 pm
this lecturer is brilliant!
October 25, 2010 at 1:18 pm
good stuff i like the lecture!!
October 21, 2010 at 5:29 pm
Very very helpful!
October 21, 2010 at 2:45 pm
ITS GREAT .. SIMPLY GREAT … IT REALLY HELPED ME ALOT
October 19, 2010 at 5:11 pm
I am a bit disappointed that they are no sessions on variances ..I am having some challenges there… can anyone help?
October 19, 2010 at 5:40 pm
if I remember correctly, you can see Variances in lectures for Paper F5
October 19, 2010 at 3:05 pm
Goosh, i just got to know about open tuition, i wish i new earlier, preparations for my june eaxams 2011 will be much much better, i am saying a BIG THANK YOU to the operators of this site, you have really helping alot of people to be better accountants. GOD BLESS YOU ALL.
October 18, 2010 at 5:56 pm
October 17, 2010 at 12:54 pm
it was wonderful , may i please know the lecturer name and his address ??
October 17, 2010 at 2:27 am
i never understood linear programming until now
October 13, 2010 at 7:48 am
May I have some explicit notes on modern accounting methods i.e Throughput,Backflush etc – it will help me a lot please.
October 1, 2010 at 11:45 am
that is very useful
September 29, 2010 at 1:04 pm
Can anyone tell me that which book is being used in this lecture??And other lectures too(F2)?
September 29, 2010 at 2:59 pm
@jaber OpenTuition course notes
October 19, 2010 at 5:50 am
Its very resourceful
September 20, 2010 at 7:21 pm
it’s really really gud…
September 20, 2010 at 2:35 pm
extremely helpful.i m preparing for this paper but iam finding it easier than class room lectures.great lecturer big up
September 18, 2010 at 11:31 pm
a lecture better than my classroom lectures …well explained…very helpful..thanku
September 18, 2010 at 12:11 pm
very nice lecture thanks a lot
annete a. nugent says
September 4, 2010 at 1:51 pm
very very good lecture.
August 11, 2010 at 8:17 pm
very helpful and very well explained.
August 26, 2010 at 9:09 pm
indeed, he’s got talent in explaining.
June 24, 2010 at 5:35 pm
great lecture and understandalbe
June 17, 2010 at 8:36 pm
Although this is something I learned years ago and never forgot, this lecture and the way is explained is incredibly simple for anybody to understand. Very good!!
June 13, 2010 at 3:28 pm
very good lecture
June 12, 2010 at 7:00 pm
Very,very helpful !
June 12, 2010 at 5:32 pm
May 30, 2010 at 2:36 am
This lecture is easy to understand and made linear programming way easier than class room’s lecture.
May 30, 2010 at 1:15 am
Asim Nawaz says
May 27, 2010 at 8:21 pm
May 26, 2010 at 1:09 pm
this lecture help me a lot
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