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ACCA F5 Linear Programming – Lecture 4 – Spare capacity and Shadow prices

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  1. What if there was no slack in labour as well. How would we find out the shadow price for materials then ? like in the equation we took both the constraints to find out the value of S and E increasing one unit of scarce resource. We took both the constraints because both are scarce resource what if only one for eg material was scarce resource.

    • According to my understanding if only material was a scarce resource we still would have taken the labour equation in order to calculate S and E for shadow price because the intersecting point includes labour with material and does not matter if labour is scarce or no

      basically the 1st equation will be the scarce resource with one extra unit

      and 2nd equation will be the other resource at the intersecting point even if it is not a scarce resource

      please let me know if understanding is right

      • But there have to be always two scarce resources for there to be an optimal solution! The intersecting point is always where the lines for two scarce resources cross – otherwise it would make no sense at all.

        Do please what the lectures again, and don’t think in terms of equations – understand what is actually happening.

  2. Hi, in this example lets say I am trying to find out the shadow price of labour. I have found that my E value is 4.75, but to find the value of S which equation do I put it back into? Does it matter? I put it back into 5S + 6E = 180, and my value for S was slightly lower at 30.30.

    Thanks
    Manisha

    • It certainly does matter. You ‘put it back into’ the other limiting constraint, which in this case is the material equation. The correct value for S is 30.5, as you can check with the answer.

  4. Dear Sir, thank you for another great lecture. Just to clarify, increasing production after calculating the shadow price would only be worth it if the extra amount to be paid for materials for example is LESS than $1.125?

    • I wanted to get the same number of S’s in both equations, so multiplying the first equation by 2.5 meant that 2S x 2.5 gave 5S.

      However there are several ways of solving simultaneous equations – you don’t have to do it my way. I find my way the easiest, but by all means do it whatever way you were taught at school. The final answer will obviously always be the same 馃檪

  6. Dear tutor, could you please explain: when we calculate shadow price of labour which equation should we use – equation 1 or equation 2 (5S+6E=181)? I’ve calculated S as 32.4 using equation 2 while in lecture notes there is another result. Thank you in advance!

  8. John from your lecture is it correct to say that the relevant cost of gaining one additional unit of a scarce resource = normal cost + shadow price. In addition, I learnt that critical (binding) constraints have no slack but do have shadow or dual price and non-critical constraints have slack but no shadow price.

  10. Sir, from mins 1:35 you begin to explain slack.
    at around 1:50 you begin with the question : Are we using all of the materials available at point B?
    You say : Yes we are and how do we know ? because we are on the materials line.

    When you say : ” We are on the materials line” in the video, i have no idea what you mean sir.
    please explain as to what exactly you are referring to.

    My best educated guess is that when you say point B you actually mean the optimum production point but then i might be wrong, i just want to be sure. do correct me if i am wrong.

    • Why on earth you need an ‘educated guess’ defeats me!!

      This is the 4th in a series of lectures working through the linear programming example. In the earlier lecture I drew the graph and labelled all the corners. The corner labelled ‘B’ was the optimal and was on the materials line.

      The lectures are meant to be watched in order – not at random.

      • Sir, when i wrote educated guess, i meant having understood from your past lectures, excuse my english, its not my mother tongue.

        For your information, i am watching all the lectures in order as provided by you.
        To go further on that point im not studying ACCA as a joke to read it in a random order.
        I believe every person is different in there own way, i personally am an anxious person actually suffering from severe clinical anxiety. Having gone through all the 4 lectures in one single sitting on a days stretch i must say i was a bit over whelmed by the time i reached the fourth lecture. Maybe this led me to ask the doubt as i wanted to be as clear as possible.

        Having that said, thank you for clarifying the doubt.

    • You do calculate the slack mathematically (from the equation), but you need to look at the graph to find out what the limiting constraints and optional solution are first.

      (There is a purely mathematical way of solving linear programming questions completely, called the simplex method, but that is not in the syllabus and you are only tested on the graphical approach.)

  12. About shadow price(Based on example 3), for instance for material constraint, can I understood it as “If we are willing to add one more unit(kg) of material, we can obtain $1.125 increase in contribution?”

  16. Thanks John. If we gain or lose one more unit of a scarce resource in production then the shadow price (the extra cost of having or losing that scarce resource) will impact on the optimum solution and ultimately the maximum contribution. It is then necessary to calculate the new production plan for S and E and their combined total or maximum contribution.

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