- This topic has 5 replies, 3 voices, and was last updated 9 years ago by
.
- Posts
This has reference to the Dec 2010 cosmetics question. There are 3 constraints, two relating to raw material and third relating to labour. Examiner has solved the equiation using labour and material, but if you solve the equation using the material you get different values for x and y.
1) silk – 3x + 2y = 5,000
2) amino acid 1x + 0.5y = 1,600
3) Labour 4x + 5y = 9,600If we solve 1 and 2 we get x = 400 and y = 1,400
If we solve 1 and 3 we get x = 1,257.14 and y= 828.58.Accordingly answer values regarding optimum contribution and shadow price also will change.
Is there any rule to follow in this regard? I don’t know whether I am wrong. But I have given the constraints correctly above.
You have to draw the graph and then move out the contribution line to find which of the corners is the furthest away from the origin. Then you know which of the two constraints need to be solved to get the highest possible contribution.
Incidentally, it is not x = 400 and y = 1400, it would be x = 1,400 and y = 400.
I really do suggest that you watch the free lecture on linear programming.
Thanks for the quick reply. Agree with the correction. I will watch the lectures.
I thought solving the equation is easier and there will be some rule when 3 constraints are given. .
RegardsNo there is no rule – you can only decide by drawing the graph (and the examiner specifically asks for the graph).
I’m confused with this question too.. after drawing the graph, in the answers, it says …
Solve using iso-contribution line
If y =800 and x = 0, then if C = 9x + 8y
C = (8 x 800) = 6,400
Therefore, if y = 0, 9x = 6,400
Therefore x = 711·11Has this just used random number just to get the contribution line, right? It doesn’t matter which numbers I substitute for C? Because I used, C=7200, to get y=900 and x=800 which I then plotted on the graph.
Also, I’m a little confused with the whole using the contribution line. Does this mean, if in the answer, the contribution line was a lot steeper, and if moved along, it intersected point “d”, we would solve the two equations which meet to form “d”?
Thanks
Yes to both questions (although it really would help you if you had watched the free lecture where I explain this in detail).
It does not matter what value you choose for C when plotting the contribution line – it is the angle/slope of the line that we need, and it will be the same whatever value for C you choose.
And yes, depending on the slope/angle of the line, if could be any one of the corners of the feasibly region that gives the maximum contribution.
- You must be logged in to reply to this topic.