Linear Programming - Spare capacity and Shadow prices - ACCA Performance Management (PM)
YouTube video
69 Comments
S
SALOME·
Sir, could you kindly clarify the below questions:
1. In the shadow price example, you noted that we only increase the constraints we want. i.e extra kilo for material and extra hour for labor if we want it. How do i determine which of the constraints to be increased and how much it will be increased for in the exam? Will this be specified? Since the example 3 did not specify these.
Also, it is possible to have a question to increase both constraints?
2. In the graph, to determine the optimum plan, its the point where the material and labor meets. What if we do not have such meeting point on a graph? How do we calculate the optimum please?
Also, you multiplied material equation by 2.5, i presume this is to have like numbers? so do i have to assume any number to multiply one of the equations to have like numbers?
J
John MoffatTutor·
1 We add 1 extra unit of whichever resource that the question is asking for the shadow price of.
No - it is not possible to increase both constraints (and it would not mean anything anyway).
2. We follow the normal rules but only one of the constraints would then be limiting (and so the optimum would be at one of the two places where the constraint crossed one of the axes).
Yes - you can use any multipliers when solving simultaneous equations like this.
A
Annabel·
Hi John,
I'm still confused as to why you didn't increase the labour demand to 181 like materials, and why you just kept it at 180? And I'm still confused as to how you know $1.125 is the most extra we would have to pay for the shadow prices bit? Thanks :)
M
Maureen·
Hi Mr John,
Why are we adding extra kilo to material but we are not adding extra hour to labor
J
John MoffatTutor·
We add an extra kg to material if we want the shadow cost of material. We add an extra hour to labour if we want the shadow cost of labour.
C
chukwudi·
The most per kg the company should be ready to pay seems a bit off or am i missing something?
J
John MoffatTutor·
Why a 'bit off'? (The shadow price is the most extra they are prepared to pay).
M
mohamed·
Hi Mr Moffat,
I just did the question in the mcq after the chapter, however I don't get why the most a company should be willing to pay is the shadow price plus the cost per material.
Would you be able to explain this to me please?
Kind regards
M
mohamed·
I found it, you've explained it in the video so just replayed it again. Apologies!
J
John MoffatTutor·
No problem :-)
A
Anjali·
can u please explain me?
M
me·
how do we know that if we change the limit of materials the optimum profit will still be at point B?
J
John MoffatTutor·
Because the materials line will move but only by a very small amount, and the angle of the line will of course stay the same.
K
Kay·
Dear Mr John,
I am confused on the shadow prices part. Can we use the labour equation 5S + 6E = 181 to calculate the shadow price instead of material equation 2S + 4E = 81? Using labour equation, the shadow price will be $0.75. Is it appropriate to use labour equation to calculate shadow price?
Please guide me on this. Thank you very much.
J
John MoffatTutor·
It depends on whether we want the shadow price of materials or the shadow price of labour.
K
Kay·
Thanks for your reply Mr John. :)
J
John MoffatTutor·
You are welcome :-)
K
Kamran·
Dear John,
Can you help me resolve one confusion. While calculating slack at the start of this video, it turned out to be zero in case of material and labour both. However, if i check the usage of material by using other method, it gives different result. What i did was that, we figured out that we are producing 30 standard chairs and 5 executive chairs. The quantity of material used in each chair is picked from the information given in question (i.e. 2 KG for standard and 4 kg for executive). When i multiply this by number of chairs produced it gives (i.e. 2*30 + 4*5) = 80 KG.
Same procedure i applied to calculate labour. Please let me where i am doing wrong.
J
John MoffatTutor·
There are only 80kg of material available and they are using all of it. Therefore there is no slack!
K
Kamran·
Oops. I am sorry. i had 100KG of available material in my mind, i don't know where it came from. Thank you for your patience to answer some silly questions.
A
Ahmad·
Hi Sir,
Is there any way to calculate the slack without referring to the graph.
thank you!
J
John MoffatTutor·
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.
S
shakir7385·
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.
J
John MoffatTutor·
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).
S
sleepybird·
Good day Mr John .
How did you get the “5” for demand. The point says 10.
J
John MoffatTutor·
I am not sure which point you are referring to. At point B where there is maximum contribution, the number of executive chairs is 5.
S
sleepybird·
I understand now.
Thank you for your lectures!
J
John MoffatTutor·
You are welcome :-)
I
Ibrahim·
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?
J
John MoffatTutor·
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.
N
naholom1990·
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.
J
John MoffatTutor·
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.
I
Ibrahim·
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.
P
Patricia·
Sir please with the spare capacity aspect I no the demand is 10 so why did u subtract the 5 from it. Not too clear. Tnx
J
John MoffatTutor·
The maximum demand is 10, but at the optimal solution we are only producing 5.
Therefore there is 10 - 5 = 5 spare demand.
P
Patricia·
Thx sir
J
John MoffatTutor·
You are welcome :-)
S
sultansultan·
Thanks I got it.
J
John MoffatTutor·
I am pleased that you have now got it :-)
S
sultansultan·
hi John,
Please can you tell from where 2.5 come and you multiply it with S & E.
A
arijfarooqi·
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?
T
Tan·
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?
T
Tan·
Example the shadow price for extra labour hr is $ 125 and the cost of the labour per hr is $45.
So the shadow price is $125 or $$170?
J
John MoffatTutor·
If the shadow price is $125, then the shadow price is $125 !!!!
It is the most extra you will be prepared to pay for an hour of labour. So if you are asked what is the most you will pay for more labour then the answer is $170 per hour ($125 more than we normally pay), but the shadow price itself is $125.
T
Tan·
Thanks John for the clear explanation. Appreciate it.
J
John MoffatTutor·
You are welcome :-)
D
deena·
Please show the questions on the screen and also explain the theory part. As explained in f7 lecture videos.
Thank you.
J
John MoffatTutor·
No - print out the lecture notes first :-)
(And all the 'theory parts' are explained the lectures!)
P
pgoyal·
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.
J
John MoffatTutor·
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.
U
umesh241182·
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.
J
John MoffatTutor·
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.
S
saiteja·
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 :)
A
alie2018·
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).
A
alie2018·
*see answer on page 93......
S
saiteja·
Thank you so much , yes I have got the same answer $0.75 , just wanted to make sure that I was doing it right .
A
alie2018·
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
A
alie2018·
John what's the effect of slack and shadow price?
J
John MoffatTutor·
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.
A
alie2018·
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.
A
alie2018·
For critical constraints there is no slack but shadow price and for non-critical constratints there's slack but no shadow price
A
alie2018·
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.
J
John MoffatTutor·
Correct - the shadow price of the non-critical constraints is therefore zero.
A
alie2018·
Thank you sir
J
John MoffatTutor·
You are welcome :-)
A
Ali Ansari·
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)
1. In the shadow price example, you noted that we only increase the constraints we want. i.e extra kilo for material and extra hour for labor if we want it. How do i determine which of the constraints to be increased and how much it will be increased for in the exam? Will this be specified? Since the example 3 did not specify these.
Also, it is possible to have a question to increase both constraints?
2. In the graph, to determine the optimum plan, its the point where the material and labor meets. What if we do not have such meeting point on a graph? How do we calculate the optimum please?
Also, you multiplied material equation by 2.5, i presume this is to have like numbers? so do i have to assume any number to multiply one of the equations to have like numbers?
No - it is not possible to increase both constraints (and it would not mean anything anyway).
2. We follow the normal rules but only one of the constraints would then be limiting (and so the optimum would be at one of the two places where the constraint crossed one of the axes).
Yes - you can use any multipliers when solving simultaneous equations like this.
I'm still confused as to why you didn't increase the labour demand to 181 like materials, and why you just kept it at 180? And I'm still confused as to how you know $1.125 is the most extra we would have to pay for the shadow prices bit? Thanks :)
Why are we adding extra kilo to material but we are not adding extra hour to labor
I just did the question in the mcq after the chapter, however I don't get why the most a company should be willing to pay is the shadow price plus the cost per material.
Would you be able to explain this to me please?
Kind regards
I am confused on the shadow prices part. Can we use the labour equation 5S + 6E = 181 to calculate the shadow price instead of material equation 2S + 4E = 81? Using labour equation, the shadow price will be $0.75. Is it appropriate to use labour equation to calculate shadow price?
Please guide me on this. Thank you very much.
Can you help me resolve one confusion. While calculating slack at the start of this video, it turned out to be zero in case of material and labour both. However, if i check the usage of material by using other method, it gives different result. What i did was that, we figured out that we are producing 30 standard chairs and 5 executive chairs. The quantity of material used in each chair is picked from the information given in question (i.e. 2 KG for standard and 4 kg for executive). When i multiply this by number of chairs produced it gives (i.e. 2*30 + 4*5) = 80 KG.
Same procedure i applied to calculate labour. Please let me where i am doing wrong.
Is there any way to calculate the slack without referring to the graph.
thank you!
But remember that you cannot be asked to draw the graph - if it is needed then it will be given you in the question.
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.
How did you get the “5” for demand. The point says 10.
Thank you for your lectures!
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?
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.
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.
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.
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.
Therefore there is 10 - 5 = 5 spare demand.
Please can you tell from where 2.5 come and you multiply it with S & E.
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?
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?
So the shadow price is $125 or $$170?
It is the most extra you will be prepared to pay for an hour of labour. So if you are asked what is the most you will pay for more labour then the answer is $170 per hour ($125 more than we normally pay), but the shadow price itself is $125.
Thank you.
(And all the 'theory parts' are explained the lectures!)
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.
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.
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.
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 :)
The shadow price tells you how much extra it is worth paying in order to get more of the resource.
thank you so much for this brilliant lecture.
With kind regards,