thank you for another great lecture, i sometimes have trouble extending the iso contribution line and realizing which is the actual point of intersection I should use. Is its worth substituting values at both points and use the one which generates the highest contribution? in this example C or D even though it is clear here.

Thank you for your lectures. I am so confident doing Linear programming with 2 constraints. However, I have revised this topic and one of the questions gave me 3 constraints. 1. Skilled labour hours 4x + 5y = 9600 2. Silk Powder 3x +2y = 5000 3. Silk Amino x + 0.5y = 1600 Lotions demand y =2000 Cream demand x – unlimited

To calculate to optimum production, the solution uses 1 and 2.

At first, I used 2 and 3. But the answer isnt the same.

Is there any reason we should use this constraints equation rather than the others?

In future you must ask this kind of question in the Ask the Tutor Forum – not as a comment on a lecture. You can’t just pick two constraints at random – you need to draw the graph in order so what the feasible region is.

Sorry just to expand on this – as we cannot be expected to draw the graph in a computer based exam, would any questions to do with linear programming be with 2 constraints only so that it would be a case of establishing the simultaneous equations then solving them?

Mr Moffat are we going to be given the value of the objective function (I.e.maximize contribution ‘C’ ) when drawing an iso-contribution line to solve for the optimal solution using the graph or we assume a value for C?

When is it feasible to use simultaneous equations to solve for the optimum production plan not using the graph?

My institute’s tutor taught this already and for some reason the way he teaches makes it hard for me to understand it but everytime i watch your lecture I understand it like magic.. Thankyou Sir Moffat! God Bless you!

Wow! We can use an iso-contribution line ( a line of equal contribution) to find the optimum solution from the graph or we take the binding constraints (in this case materials and labour) to formulate another equation that can be used to find the values of S and E. This then can be used to calculate the maximum contribution. Thanks so much John for clarity in this topic.

Look at the graph again, its certainly not in the feasible region, another way is to put those numbers for S and E into one of the binding constraint equations.

2S + 4E <= 80, if we were to make 24 S and 10 E, the equation would be:

2(24) + 4(10) = 88 which is as far as I know not less than or equal to 80

Firstly, thank you so much for your excellent lectures.

One thing I struggle with is getting a parallel outward shift of my ruler to the furthest point of production within the feasible region.

I’m sorry if this is a silly question, but will the furthest point always coincide with the point where two of the limiting factors intersect (like it did in your example) or is it possible that the parallel outward movement of the objective function line could land on a point/corner of the feasible region before reaching the point where the two limiting factor lines intersect?

I’m really sorry if this has not been worded clearly/is a silly question.

The furthest point away from the origin (the optimal point) will always be where two of the constraints intersect – i.e. at one of the corners of the feasible region. The point of moving out the contribution line while keeping it parallel is in order to identify which of the corners is the best one.

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loukasierides says

dear Sir,

thank you for another great lecture, i sometimes have trouble extending the iso contribution line and realizing which is the actual point of intersection I should use. Is its worth substituting values at both points and use the one which generates the highest contribution? in this example C or D even though it is clear here.

John Moffat says

Yes – that is fine (provided you can do it quickly 馃檪 )

In the exam you cannot be asked to draw the graph, but you can be given a graph and asked to solve it.

loukasierides says

oh i see ! i thought this time I would i actually get to draw a graph! thank you very much!

John Moffat says

You are welcome 馃檪

khanumishq says

Why is the optimum production plan not at point A? Is it because that is not the intersection point of two constraints?

John Moffat says

It is because point B is the furthest point from the origin when you move out the iso-contribution line keeping in parallel.

I do explain this in the earlier lectures.

loukasierides says

Dear Sir,

thank you for another incredible lecture, i wish they did ask me to draw this graph, it would be easy marks.

John Moffat says

You are welcome.

angelaht says

Hi John,

Thank you for your lectures. I am so confident doing Linear programming with 2 constraints.

However, I have revised this topic and one of the questions gave me 3 constraints.

1. Skilled labour hours 4x + 5y = 9600

2. Silk Powder 3x +2y = 5000

3. Silk Amino x + 0.5y = 1600

Lotions demand y =2000

Cream demand x – unlimited

To calculate to optimum production, the solution uses 1 and 2.

At first, I used 2 and 3. But the answer isnt the same.

Is there any reason we should use this constraints equation rather than the others?

This question I got from BPP Exam kit.

Thanks,

Angela

John Moffat says

In future you must ask this kind of question in the Ask the Tutor Forum – not as a comment on a lecture.

You can’t just pick two constraints at random – you need to draw the graph in order so what the feasible region is.

angelaht says

Thank you John

John Moffat says

You are welcome 馃檪

daynaellis says

Hi,

Sorry just to expand on this – as we cannot be expected to draw the graph in a computer based exam, would any questions to do with linear programming be with 2 constraints only so that it would be a case of establishing the simultaneous equations then solving them?

Thank you.

John Moffat says

No – there can be more than two constraints. You will not be expected to draw the graph, but a graph may be given you as part of the question.

Samuel Koroma says

Mr Moffat are we going to be given the value of the objective function (I.e.maximize contribution ‘C’ ) when drawing an iso-contribution line to solve for the optimal solution using the graph or we assume a value for C?

When is it feasible to use simultaneous equations to solve for the optimum production plan not using the graph?

sxhawty says

My institute’s tutor taught this already and for some reason the way he teaches makes it hard for me to understand it but everytime i watch your lecture I understand it like magic.. Thankyou Sir Moffat! God Bless you!

John Moffat says

And thank you very much for your comment 馃檪

Samuel Koroma says

Wow! We can use an iso-contribution line ( a line of equal contribution) to find the optimum solution from the graph or we take the binding constraints (in this case materials and labour) to formulate another equation that can be used to find the values of S and E. This then can be used to calculate the maximum contribution. Thanks so much John for clarity in this topic.

John Moffat says

You are welcome 馃檪

haidershah says

if we go with 24S and 10E the it comes to 234 still in the feasible Region

24 * 6 = 144 and 10* 9 = 90

144+90 = 234 so its more then 225 please comment

Syed Muhammad says

Look at the graph again, its certainly not in the feasible region, another way is to put those numbers for S and E into one of the binding constraint equations.

2S + 4E <= 80, if we were to make 24 S and 10 E, the equation would be:

2(24) + 4(10) = 88 which is as far as I know not less than or equal to 80

alaccountancy says

Hi

Firstly, thank you so much for your excellent lectures.

One thing I struggle with is getting a parallel outward shift of my ruler to the furthest point of production within the feasible region.

I’m sorry if this is a silly question, but will the furthest point always coincide with the point where two of the limiting factors intersect (like it did in your example) or is it possible that the parallel outward movement of the objective function line could land on a point/corner of the feasible region before reaching the point where the two limiting factor lines intersect?

I’m really sorry if this has not been worded clearly/is a silly question.

Thank you.

John Moffat says

The furthest point away from the origin (the optimal point) will always be where two of the constraints intersect – i.e. at one of the corners of the feasible region.

The point of moving out the contribution line while keeping it parallel is in order to identify which of the corners is the best one.