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Linear Programming part 2 – Spare Capacity & Shadow prices

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    • I did it for both labour and for material. However, since material is not a binding constraint the shadow price is obviously zero.

      In the exam you will be told which resources to calculate the shadow prices for.

    • You identify it by moving out the contribution line (keeping it parallel) as far as you can from the origin, without leaving the feasible region.

      (If you want me to answer questions, then please ask in the F5 Ask the ACCA Tutor Forum – it is not possible for me to always read all the comments beneath lectures 馃檪 )

  4. There is no specific rule about how many decimal places (unless, obviously, the question specifies).
    Generally keep to two decimal places. It doesn’t matter if it impacts a later answer – the marks are for the workings, not for the final answer.

    (If you want me to answer a question, then please post it in the Ask the ACC Tutor forum – I cannot always read every comment under the lectures).

  5. hi prof moffat,
    i am practising the questions and got a problem. for those equations don’t give an integer, how many decimals shall we keep? i saw the exam bank kept two, but is it mandatory?since the value will impact the further calculation for the contribution and also shadow price. thank you very much for a clarification and thx for the great lectures as well!

    Xiaowen

  6. hi sir i was just wondering how come the demand is less than 10?because looking at the graph the demand line is also part of the feasible region.and when you did material and labour you said there was no slack because it on the labour and material line so how come there is slack for demand beacuase it is also part of the feasible region

      • In the last paragraph (before workings) it explains that at point D they would be making 4000 units of Y.
        From the beginning of the example, we know that each unit of Y needs 5 kg of material.
        So….4000 units needs 20,000 kg.

  12. Thanks, the lecture was very insightful!
    Just a question though, at the end where you mentioned that shadow price for demand of E would be zero due to slack.
    What if that was not the case and demand is 10, I was wondering how would the calculation or approach be like?

      • If you look again at example 1 in the chapter, but this time suppose the maximum demand for executive chairs was 4 (instead of 10).
        The graph in the answer would stay the same except that the demand line would move to the left.
        It will mean that the feasible area will be A, D, O, and the point where the demand line crosses the labour line. (The existing point B would no longer be feasible).

        The new optimum point would be where the demand line crosses the labour line (which would be producing 4 executives and 32 standard chairs) and the new maximum contribution would be $312.
        This time, the material constraint would be redundant (and the shadow cost of material would be zero). However the demand would be limiting – if we could increase the maximum demand by 1 unit then we could change the production and make more contribution. The extra contribution from having demand for 1 more unit would be the shadow price.

  13. Dear Sir,
    I think your video cover all the complex area of the syllabus. But I found your examples as easy than compare to examination level or even in Kit. After having lectures I need to study from the study text and go through the examples which takes lots of time. Even I dont get time to have Kit questions. This way I can only cover 1 or 2 topics per week.

    The other question is that as I am very poor boy, so after completing my papers till f7. Will I be able to have any job? Which country do I go that is cheaper for students and can let me study with cheap costs and a job.

    Is there any solution? By the way Opentuition is a miracle for me.

    Many Thanks

    • The lectures do cover what you need for the exam in terms of the technique. The examples that I go through are certainly enough in terms of the technique, but the wording is deliberately kept more simple than the wording in the exam (because I am trying to make sure people understand the technique). Also exam questions often examine more than one topic in the same question – I can only teach one topic at a time in lectures 馃檪
      On courses, after I have finished the lecture the class then work through some past exam questions.
      If you look at the main Paper F5 page on this website you will find some lectures working through past exam questions – you might find this saves you time and saves you having to work through the Study Text so much.

      I cannot really help with regards to jobs and with regard to countries with cheap costs etc.. A lot depends on which country you live in. Courses are pretty expensive everywhere 馃檨

  14. Dear Sir,
    One question: The Point “B” that we gained, came from the simultaneous equation. I mean “2S+4E=80 and 5S+6E=180”. So why we used our graph for B? I mean if we simply could use this equation that was obvious from the question then why we need to put stress on graph? Then we cant certainly try the other farther points.

    • The problem is that if you did not have the graph then you would not know whether the optimal point was at point A, B, C or D. Depending on the angle of the objective/contribution line it could be any of them. Also, what about the point where the labour line crosses the demand line? This is not a feasible solution, but without the graph this would not be obvious.

      Also, in the exam you will almost certainly be required to draw the graph – in which case you obviously have no choice. (And on at least one occasion the graph was given in the question – in this case you obviously were not required to draw it yourself, but you did need to know how to interpret it.)

  15. Hi John,

    Good day to you 馃檪 I just started using opentuition for my study after June’13 exams. I thoroughly enjoyed your presentation in every chapter. Your delivery was so engaging. By any measure you are a very effective lecturer 馃檪 I appreciate your time, your patience and your ability to make a dry subject interesting 馃檪 Thank you so much, sir.

    I have already started doing revision. I’m using the latest BPP revision kit. I have something not understand about Linear Programming. I stuck in questions 24 (Question 3, December 2010 exam). In part (a), after draw the graph, we need to find the optimal solution using iso-contribution line then solving the simultaneous equations for these constraints :
    4x + 5y = 9,600 x 3
    3x + 2y = 5,000 x 4

    My questions is why we need to multiply the constraints by 3 for skilled labour constraints and multiply 4 for silk powder constraints? And why not multiply by 1 or 2? How we know when we need to multiply the constraints?

    Once again, thank you for your time and for always going the extra mile as a lecturer. I appreciate it more than you will ever know 馃檪

    Enjoy your weekend 馃檪

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