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I have done this number using the graphical method as requested by the Examiner.
I also wanted to try it using the simultaneous equation method. I have used the constraints of ash ( materials) and that of skilled labour, however i don’t get the same results how can i go over it.Thanks
There is no such thing as the simultaneous equation method! The only two ways of solving linear programming questions are the graphical method and the simplex method (which is not in the syllabus).
With the graphical method you need to always use simultaneous equations to find the optimal mix of products at the point where the two lines cross.
From the graph you can tell that the highest contribution occurs where the demand for S line crosses the labour line.By all means check where the materials line crosses the labour line, but if you calculate the total contribution it will be lower – it is not the optimal solution.
Have you watched my lecture on linear programming?
Dear John,
Thanks for the response.
I get confused when you say “There is no such thing as the simultaneous equation method!”I see in the syllabus under limiting factors item number 3,
c) Formulate and solve multiple scarce resource
problem both graphically and using
simultaneous equations as appropriate.[2]
Please clarify on that.As I replied before, you need to be able to use simultaneous equations to be able to find the values at the optimal point on the graph. The only reason that she has written it the way she has is that in recent exams you have been given the graph (instead of having to draw it yourself, but still needed to use simultaneous equations.
It is not a separate method – you always need the graph otherwise you do not know which point to check (as you found out yourself using materials and labour).Thanks again for the response.
So if i always need to use simultaneous equations to be able to find the values at the optimal point on the graph, how about the ISO contribution line. I thought this is what it helps with. You drag it outwards and the point when it last exists the feasible region is always the optimal point.
According to you response is it okay to ignore the Dragging of ISO line and i simply keep testing the points of intersection at the edges of the feasible region as i compare the contributions at each until i find the highest contribution, and then conclude that this is the optimal point?
You can either use the ISO contribution line to find the optimal point – and then use simultaneous equations to find the values at that point.
Or you can find the contribution at each of corners of the feasible region (again using simultaneous equations to find the values) and the optimal is the one giving the highest contribution.In both cases it is the graphical approach and you need to have the graph, and in both cases you need to use simultaneous equations – the approach has exactly the same logic in both cases.
(The reason you got a different answer using materials and labour is because that intersection is outside the feasible region)Usually you can do it either way, but make sure you can do it using the iso-contribution line because it could be specifically asked for. Otherwise it is whichever you find quickest – obviously both give the same answer.
Thank you very much.
This is help full.Now this is just a navigation issue.I find a challenge I find it hard to trace my question from the list that appears under ask the Tutor. I have been using the email alerts to get it.
What is the easiest way to use this site
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