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

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.

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.

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.

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

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!

If you are calculating the shadow price of labour, then you re-write the labour constraint adding 1 hour to the previous maximum. Then you recalculate the optimum mix and the new maximum contribution.

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.

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.

I’ll like to know from the way you explained the slack, does it mean there is no mathematical way of generating the slack except by looking at the graph?

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.)

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?”

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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abhishekbakshi says

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.

abhishekbakshi says

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

John Moffat says

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.

manishatai says

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

John Moffat says

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.

jihane says

Thank you very much …very clear and well explained

You are the best teacher

John Moffat says

Thank you for your comment 馃檪

loukasierides says

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?

John Moffat says

Correct

loukasierides says

thank you very much

John Moffat says

You are welcome

abdulwahabawais says

about shadow price :while calculating/multiplying the equation 1:from where did you get 2.5 ? please explain

John Moffat says

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

gregapetrov says

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!

John Moffat says

If you are calculating the shadow price of labour, then you re-write the labour constraint adding 1 hour to the previous maximum. Then you recalculate the optimum mix and the new maximum contribution.

gregapetrov says

Thank you very much for clarification!

John Moffat says

You are welcome 馃檪

maqmukul says

Sir

i am confused about no spare demand

can u explain please?

John Moffat says

There is no spare demand because they are producing that product to meet the full demand.

Samuel Koroma says

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.

John Moffat says

No – the normal cost plus the shadow price is the most you would be prepared to pay for one extra unit.

Your second sentence is correct.

Samuel Koroma says

Noted John – the ‘most’ the business would be willing to pay for the additional unit of a scarce resource. Thanks for the clarification

John Moffat says

You are welcome 馃檪

nyansinde11 says

Great lecture and presentation, thanks John.

John Moffat says

Thank you for the comment 馃檪

surajnagesh says

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.

John Moffat says

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.

surajnagesh says

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.

John Moffat says

You are welcome, and sorry for misunderstanding 馃檪

asantej says

I’ll like to know from the way you explained the slack, does it mean there is no mathematical way of generating the slack except by looking at the graph?

John Moffat says

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.)

wajinow says

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?”

John Moffat says

That is correct.

wajinow says

Thank you very much!!!

John Moffat says

You are welcome 馃檪

arlene022178 says

Thank you so much John. Really appreciate it.

John Moffat says

you are welcome 馃檪

iyamu says

Excellent lecture piece, clear and sound English plus good methodology.

But why are you not taking Financial reporting?

John Moffat says

I teach 5 papers and that is quite enough 馃檪

lisa94 says

Thank you for this lecture. well understood

John Moffat says

Thank you for the comment 馃檪

Samuel Koroma says

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.

John Moffat says

But that is what I do in the lecture 馃檪

Samuel Koroma says

Yes for sure. I am only summarising what I gathered from your presentation