1. avatar says

    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?

    • Profile photo of John Moffat says

      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.

      • avatar says

        Oh I see, thank you. And my apologies for asking something you answered in the lecture. So much information to try and retain!

  2. Profile photo of Lilit says

    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.

  3. avatar says

    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.

  4. avatar says

    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.

    • Profile photo of John Moffat says

      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.

  5. Profile photo of Imran says

    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..

      • Profile photo of John Moffat says

        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.

  6. Profile photo of Karina says

    Dear John,
    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?

    • Profile photo of John Moffat says

      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.

  7. avatar says

    Hiii sir, your lectures juz awesome ūüėÄ

    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”?

    • Profile photo of John Moffat says

      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 :-) )

  8. avatar says

    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 :)

  9. avatar says

    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?

    Thx :)

  10. avatar says

    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.

  11. avatar says


    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!

    Thank you

    • Profile photo of John Moffat says

      Several reasons!

      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!

    • Profile photo of John Moffat says

      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.

  12. avatar says

    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.


    • Profile photo of John Moffat says

      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)

  13. Profile photo of Gabriel says

    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.

    • Profile photo of John Moffat says

      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 :-)

  14. avatar says

    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!

    • avatar says

      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.

      • Profile photo of John Moffat says

        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)

    • Profile photo of John Moffat says

      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 :-)

      • Profile photo of John Moffat says

        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.

  15. avatar says

    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.

    • Profile photo of John Moffat says

      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 :-)

  16. Profile photo of Mahoysam says

    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!

      • Profile photo of John Moffat says

        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.

  17. avatar says

    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

  18. avatar says

    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?

  19. avatar says

    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!!

    • Profile photo of John Moffat says

      @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.

      • avatar says

        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.

      • Profile photo of John Moffat says

        @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)

  20. avatar says

    Dear tutor,
    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???

  21. Profile photo of sawnryz46 says

    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?

  22. avatar says

    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.

Leave a Reply