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Linear Programming part 2 – Spare Capacity & Shadow prices

VIVA

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    • When the constraints are less than are equal to (as is usually the case) then the slack is any unused amount of the limited resource.
      When the constraints are greater than or equal to, then the surplus is the extra being used over and above the constraint.

    • Any number. You can solve the simultaneous equations any way you like – I do it the way that I was taught at school, but if you were taught another way then that is fine – the final answer will be the same.

  5. thank you very much for your lectures it helps a lot
    can you briefly explain why you used the material 2s+4e< 80 to calculate 2.5 rather than labour 5s+6e<180. I was thinking maybe it's a better rounding off of figure

    2s+4e=80
    5s+6e=180
    5s+10e=200 why 2.5 & why material instead of labour
    0+4e=20/4
    e=5

    • If there is no slack then the amount we are prepared to pay is the normal cost per unit plus the shadow cost (which is what I have shown in the lecture for materials and labour which have no slack).

      (If there is slack then we would not pay anything because having more would not allow us to produce more of the products)

  7. Lovely lecture as usual sir! However, my question is… How do you reach maximum demand in this situation seeing that we are not meeting demand for product E. Is there a way of doing it while maintaining or increasing contribution? Thanks 馃檪

    • I am not quite sure I understand you.

      We are not trying to meet the maximum demand, we are trying to get the maximum contribution possible (without producing more than we can sell). It turns out that maximum contribution in this question is achieved by producing fewer of E (and therefore using resources to produce some of S). If we decided to produce maximum E’s, we would end up producing fewer S’s (it would be a point C on my graph) and the total contribution would be lower.

  9. Hello sir john ,
    I have a request. could you please provide us additional set of question for f5 revision mock exams(Section 1) because i have done many time that questions.. It’s my humble request if you can arrange another revision mock exam for f5 . thanks

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

      There are already well over 100 question in the bank of questions that the test is drawn from. The test selects 20 questions at random and so you should not be getting the same questions each time – if you are then try clearing the cache on your browser.

      There is no intention to increase the size of the bank at the moment.

      I assume you have a Revision Kit from one of the ACCA approved publishers (if not then you should buy one) and they contain plenty more questions to practice on.

  10. Can you please tell me how there is a shadow price for labour, and materials has slack. In both cases, E < demand. At 4.75 and 5.625. Demand is 10.
    I would have thought both had a shadow price?

    I am following very closely, but it just does not make sense to me. Thank you in advance.

    • Materials does not have slack (I actually write ‘no slack’ against it on the screen!).

      Labour and materials both have a shadow price and both shadow prices are calculated in the lecture.

      It is only with the demand that there is slack.

    • For there to be no slack for the demand, it would mean the the optimal mix would have been at corner C (if there is no slack, then the optimum must be at a corner where demand is one of the lines). (That would only happen if the contribution line was different).

      Then you would carry on the same way as usual and calculated how the optimal mix would change the demand was 1 unit more. The shadow cost would be the extra contribution generate.

    • If you are meaning guessing a contribution in order to be able to draw the contribution line, then it won,t affect anything else at all. All we need is the angle/slope of the line and that will be the same whatever value of contribution you choose.
      I think it will be helpful for you to watch the lecture again.

      • Yes sir i watch the lecture full,but there is one test that is give at the end of notes,this creating problem for me , how the answer is 6.7 ,you add simply shadow price and cost of material Z , but why you add only these two values.whats the reason behind this. (page 37 on notes )Thank you

      • The shadow price is the most extra that we would be prepared to pay for one extra unit of the limited resource.
        The current price is $3 per kg.. The most extra we are prepared to pay is $3.70 per kg..
        Therefore the most in total we are prepared to pay is $6.70 per kg..

        I do actually stress this in the lecture and explain why.

    • The shadow price is the most extra that you would be prepared to pay for one extra unit of the limited resource.
      It is calculated by taking one extra unit and calculating the extra contribution that would be earned.
      If there is slack demand, it means that we are already producing less than the limit, so even if the limit on demand was increase by 1 to 11, we couldn’t produce any more and therefore could not make any more contribution.

  19. This lecture keeps stopping after 7 mins and will not play any further. I have watched the previous lectures with no issues.
    I have updated my flash player and cleared the history/cache etc and still stops at 7 mins – any ideas on what else I need to do – to be able to watch the lectures.

    Thanks
    Shelley

  20. Hi Sir,

    About shadow pricing, How the extra contribution is regarded wholly to the cost? If the contribution is in whole becoming the cost, there is no point to stretch the additional constraint. Because the benefit all becomes the cost.

    • What you say is true.
      That is why the shadow price is the most extra we are prepared to pay for one extra unit of the limited resource.
      So…..provided we can get it for less then it is worth having (because the total contribution will increase).

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