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Linear Programming – Spare capacity and Shadow prices – ACCA Performance Management (PM)

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    • No. You need the graph to know where the optimum point is and to know which contraints are binding and which are not.

      But remember that you cannot be asked to draw the graph – if it is needed then it will be given you in the question.

  2. Dear John,

    Two questions related to shadow pricing:
    1) Why we did not check the contribution by increasing the demand from 5 to 6? I know the contribution was max. at demand 5 but same was the case with material and labour. They were also generating maximum contribution but we still calculated their shadow price.

    2) Why we taken only one extra KG of material to check what extra price we need to be to pay. May be if we have taken to extra KG it may have generated the contribution higher than the contribution generated through one extra unit. e.g. contribution generated through one extra unit was $2 however if we have taken two extra units then contribution may be higher than $4.

    • In answer to both questions, the definition of the shadow price is the most extra that we would be prepared for one extra unit of the limited resource (not one extra unit of the products because that would mean nothing).

  5. Dear John,
    In that example that you have already explained in that lecture we have only 2 types of limitations so it’s easy to solve, but in case of existing 3 or 4 how can we solve it?

    • There are three limitations (constraints) in my example, not two!! The more constraints then the more lines on the graph – the approach does not change.

      If you are actually meaning more than 2 products, then (as I explain in the lecture) it needs another technique which is not examinable.

      Also, remember that you cannot be asked to draw the graph in the exam but you are expected to understand it.

  6. What I dont understand about the shadow price is if we are prepared to pay an extra amount equal to the extra contribution that we are supposed to get for having an extra unit of a scarce resource, how does that make any business sense. I mean what is the point if at the end of the day our profit will be indifferent?
    The other thing, when you calculated the optimum production, did you use both the labour and material constraints because their lines both crossed at point be or that is always how it is calculated? Because that is were my struggle is. I just have the difficulty of identifying the point in the feasible region that can maximise our objective. Let me say our optimum point was at point C, will we still use both equations in calculating our optimum production?

    I hope you will get back at me because I will be writing in July and the issues I have highlighted are a pain on my neck.

    • With regard to the shadow price, it is the most extra that you would be prepared to pay for one extra unit of the limited resource. Certainly if you did pay that much extra then there would be no affect on the profit, but you need to know the ‘limit’ because you will have to pay more for an extra unit (otherwise it wouldn’t have been limited) and you will only buy it if the extra cost is less than the shadow price.

      As far as the optimum point is concerned, you decide what the point is by moving out the objective line. It will always be one of the corners and you then solve the two equations at that corner. It could be any of the corners and which two equations depends on which corner it is.

      If you have more questions then please ask in the Ask the Tutor Forum and not as a comment here. I do not always see comments here, but I always answer forum questions within 24 hours.

  7. Hello John sir,
    How are you?
    I hope you are doing very well,
    I have studied this topic in my university and never gotten it but after watching your informative lecture i have gotten very well,
    Thank you John sir for your appreciated time and your effort thank you so much.

  11. hello,
    to clear a concept, tell me if i am right or wrong

    shadow price is the extra contribution that we are earning from the extra whatever resource we are paying for, right? So, that contribution is the most extra that we are ready to pay before we go into loss?

  12. Hi John

    I am very confusing about the Shadow Price. As you mentioned in the lecture, the shadow price is the most extra we would be prepared to pay for extra unit of limited resource, am i irght?
    The most extra is the different better new and old contribution + cost of the limited resource?

  14. Hello John

    Can you please elaborate a bit more how for labour shadow price, it come to the conclusion

    ‘ The Shadow price of demand for executive chairs is $0, because there is already spare demand.

    • These are two separate things. The labour shadow price is calculated in the answer that is printed in the lecture notes.
      The show price for chairs is zero because they are not producing full demand and they won’t produce any more (and therefore earn no more contribution) even if the demand were increased.

  15. hi, i just enrolled for ACCA and looking for strong support. Could you please suggest which study material should I use? As I am looking for exemption but not yet confirmed. Hoping to give exam for PM.

    • In future please ask this kind of question in the Ask the Tutor Forum, and not as a comment on a lecture.

      If you are watching my free lectures then you do not really need a Study Text,because the lectures are a complete free course. However a Revision Kit is essential because practice is vital to passing the exam. You should use books from the ACCA approved publishers – either BPP or Kaplan.

  16. Hi John ,

    I would like to know the answer for the shadow price of labour cost per hour as I have calculated but cannot locate it in the notes or the end of the lecture video.

    Thank you sir for the excellent lecture 🙂

    • Shadow price was only calculated for material constraint in John’s presentation. The labour constraint was left out because it would have been the same approach using simultaneous equations. However, the shadow price for labour was calculated as $0.75 (see answer at page 93 of the lecture notes).

      • Thank you so much , yes I have got the same answer $0.75 , just wanted to make sure that I was doing it right .

      • You’re most welcome. Don’t you think that we can be study buddy. I will be attempting PM in December 2018. My WhatsApp is +23288985838. Thanks

    • As I explain in the lecture, resources are virtually never completely limited in real life – you can always get more but you will have to pay a higher price. For example, getting more than the normal labour will mean paying overtime and therefore paying more per hour.

      The shadow price tells you how much extra it is worth paying in order to get more of the resource.

      • Okay. Thanks John. So we can only calculate shadow prices for critical (or binding) constraints right. I made to understand from your lecture that slack can also be applied to a product and not only resources for example in our example the demand for E.

      • For critical constraints there is no slack but shadow price and for non-critical constratints there’s slack but no shadow price

  18. Thanks John well explained. Shadow price is only applicable to critical (binding) constraints that give rise to the optimal solution as there is no slack for these resource lines.

  19. what a brilliant explanation for shadow price,understood that for every extra unit of limited resource the most extra we would pay is the difference of revised contribution and old contribution (assuming that the price per kilo is same)

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