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# D2 6th June 2013 Watch

1. (Original post by NiceToMeetYou)
Could someone confirm the following please?

For transportation problems it'll only ever be maximise

We will only have to maximise a linear programming problem

Allocation can be maximise or minimise

Game theory LP will only be maximise
Transportation problems will always be to minimise the total cost.

Linear programming problems involving simplex will only every be maximising.

Allocation problems could be maximising or minimising.

Game theory LP will always be to maximise (why would you want to minimise your winnings? )
2. (Original post by Miken Moose)
If the problem is balanced (i.e. total supply = total demand), then the constraints should be equalities. This is because all of the demand must be met, you cannot have less delivered than what is demanded.

Additionally, since all demand will be met, this means that all supply will have to be used (remember that in a balanced problem, total supply = total demand). Therefore these constraints should be equalities too.

The only case when you should have inequalities is when you have an unbalanced problem (total supply > total demand). In this case, the total demand must still be met and so these constraints should still be equalities. However, since there is more supply than what is needed, the supply from each depot will not necessarily be used up so these should be inequalities.

I hope this clears it up for you
It's funny that in the text book they use inequalities for a balanced problem :/
Also, is it possible to get an unbalanced problem where demand>supply, or not, because I doubt it would be possible realistically to add a dummy supply point
3. (Original post by Matt_payne)
[...] is it possible to get an unbalanced problem where demand>supply, or not, because I doubt it would be possible realistically to add a dummy supply point
Well... I don't know, but I would have guessed "no", simply because the problem is not solvable in the practical sense - I mean, forget the algorithm, if there isn't enough supply you can't meet the demand.

If it does come up, I would be a little surprised, but I guess you'd just treat it with the analogous logic as for the 'traditional' unbalanced problem.
4. (Original post by Arsey)
If I could predict the future I wouldn't be here now

I don't think anything will come up that hasn't come up before. However, they could ask you to tabulate the LP GT question (I cannot see them ever asking to then follow through with Simplex).

LP max allocation question.

GT question where there is a stable solution. GT where they ask you to find the best strategy for player B after going through the well diagram method for player A.

I wouldn't be surprised if short cuts appeared on the TS question.

An initial degenerate solution when using the NWC method on transportation.

My money would be on a minimax, maximum (easier) dynamic programming question.

I wouldn't be surprised if super source / super sink makes an appearance. Also on flows maybe a sink that is in the middle of the network.

With all that been said, the new international papers mean that two papers will be written side by side. So it is likely one will have NN, the other will have short cuts. One will have LP on GT, the other LP on allocation or transportation. etc

As long as we get the next instalment of agent goodie, I will be happy.
Hi could you help me on this question i think the markscheme is wrong
Thanks,
Smith
5. Could anyone try this flow question i think the mark scheme is wrong

Thanks,
Smith
6. (Original post by Knoyle quiah)
Sorry can you explain this way, is it what i have attached??
Hi I have attached an example of the method I use to find the value of a cut. Take C1... when looking at the direction that flow goes down the arc.. the orange line is cut first on EG, EH, BF therefore the cut = 35
Attached Images

7. (Original post by Knoyle quiah)
Part C only: I thought you would increase blending because there is slack available?? why does mark scheme say opposite??
I'm not sure if I'm right here, but I don't think you're increasing anything, you're increasing the time available for them. So you wouldn't increase the time available for blending if there is already slack.
That's just how I see it, I'm not sure if that's right :/
What paper was that question from?
8. (Original post by Miken Moose)
If the problem is balanced (i.e. total supply = total demand), then the constraints should be equalities. This is because all of the demand must be met, you cannot have less delivered than what is demanded.

Additionally, since all demand will be met, this means that all supply will have to be used (remember that in a balanced problem, total supply = total demand). Therefore these constraints should be equalities too.

The only case when you should have inequalities is when you have an unbalanced problem (total supply > total demand). In this case, the total demand must still be met and so these constraints should still be equalities. However, since there is more supply than what is needed, the supply from each depot will not necessarily be used up so these should be inequalities.

I hope this clears it up for you
If you add a dummy to equate the supply and demand then would it be equalities?
9. (Original post by ChelseaSam)
If you add a dummy to equate the supply and demand then would it be equalities?
That's right.
10. (Original post by Miken Moose)
That's right.
Thanks for the help. I presume the textbook is incorrect?
Attached Images

11. Yeah there are many mistakes in the D2 textbook, and that is one of them.
12. (Original post by Miken Moose)
Yeah there are many mistakes in the D2 textbook, and that is one of them.
Hi could you help me on the flow question posted please
Thanks,
Smith
13. (Original post by brittanna)
I'm doing STEP I and AEA. I've been too scared to do any mechanics beyond M2 . In mocks, my marks seem to range from around 60 to 75. The only problem is that it already takes me long enough to complete a paper (damn you Simplex ) so I can't really afford to spend much longer on the questions than I already do, especially if I need to take into account table drawing time! It took me a lot longer than a Sunday afternoon to learn this . Do you need a decent grade in this, or are you just doing it to get the additional further maths qualification?
(Original post by Miken Moose)
Yeah I'm doing D2, M3-5 and S3-4. Fun stuff S4 is easy? I find it quite hard to not fall asleep to.
Oh awesome, how are you getting on with them? I'm sitting all three STEP exams Mmm mechanics does get a little heavy! M3 and M5 have some rather tricky aspects (referring to the fact you are expected to directly derive integrals... without using analysis or any rigour... which I find rather unsatisfying and non-instinctive :/ ) Well that's not too bad, I think it's one of those exams you can ace if you just fill your head with the stuff the day before (retaining the information long-term is the tricky part since none of it is likely to get used outside of D2 revision!) You don't need to draw tables! Look at the answer booklets! ..what a sunday afternoon and evening..? I just find all the decision modules rather straightforward, plus they all seem like 'games'. All I see it as doing is memorising (uselessly overcomplicated) information like sudoko strategies or something
Spoiler:
Show

If we were actually given these problems, we could easily find and develop our own methods to solve them that would be much quicker and yet we are forced to use a more generalised method. Unfortunately the generalised methods are not properly defined or rigorously presented (e.g. that so-called "proof" of the so-called "stable solution theorem" is a simplified version of the actually proof which gave Josh Nash a Nobel Prize in 1994 )

No I don't particularly need a decent grade in it. Well, Cambridge have asked that I get an A in additional further maths which I'm pretty sure is just busy-work because they know I will get that and, even if I didn't, if I had the right grade in STEP they wouldn't turn me away. I got 100UMS in S2 in January so the pressure is really off with AFM this summer

Oh awesome, I'm doing all of those except M3 (which I did last summer). HAHAHA that certainly made me chuckle!
14. (Original post by Jkn)
Oh awesome, how are you getting on with them? I'm sitting all three STEP exams Mmm mechanics does get a little heavy! M3 and M5 have some rather tricky aspects (referring to the fact you are expected to directly derive integrals... without using analysis or any rigour... which I find rather unsatisfying and non-instinctive :/ ) Well that's not too bad, I think it's one of those exams you can ace if you just fill your head with the stuff the day before (retaining the information long-term is the tricky part since none of it is likely to get used outside of D2 revision!) You don't need to draw tables! Look at the answer booklets! ..what a sunday afternoon and evening..? I just find all the decision modules rather straightforward, plus they all seem like 'games'. All I see it as doing is memorising (uselessly overcomplicated) information like sudoko strategies or something
Spoiler:
Show

If we were actually given these problems, we could easily find and develop our own methods to solve them that would be much quicker and yet we are forced to use a more generalised method. Unfortunately the generalised methods are not properly defined or rigorously presented (e.g. that so-called "proof" of the so-called "stable solution theorem" is a simplified version of the actually proof which gave Josh Nash a Nobel Prize in 1994 )

No I don't particularly need a decent grade in it. Well, Cambridge have asked that I get an A in additional further maths which I'm pretty sure is just busy-work because they know I will get that and, even if I didn't, if I had the right grade in STEP they wouldn't turn me away. I got 100UMS in S2 in January so the pressure is really off with AFM this summer

Oh awesome, I'm doing all of those except M3 (which I did last summer). HAHAHA that certainly made me chuckle!
I meant because i'll have wasted all of the ones they give you from making mistakes .
Your offers conditional of AFM . That's a bit harsh, but yeah, they aren't going to not give you a place if you don't get an A in D2, especially if you're getting S's in STEP .

I need 86 in either D2 or FP2 (I got 94 in S2 Jan), but I think i'm more likely to meet it in FP2.
15. I dont think the textbook is incorrect, it doesnt explicitly say that demand and supply have to be met. More specifically it isnt a practical problem. Its been formulated as a linear programming problem and so there is a feesible region in which a range of values can lie up to a maximum. Think about it in real life, when do we ever have a situation where supply meets demand and vice versa?

Im sticking to the textbook on this one, I know the textbook can have mistakes sometimes but this would've been a huge oversight considering theres only one example.

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16. (Original post by JayJay95)
I dont think the textbook is incorrect, it doesnt explicitly say that demand and supply have to be met. More specifically it isnt a practical problem. Its been formulated as a linear programming problem and so there is a feesible region in which a range of values can lie up to a maximum. Think about it in real life, when do we ever have a situation where supply meets demand and vice versa?

Im sticking to the textbook on this one, I know the textbook can have mistakes sometimes but this would've been a huge oversight considering theres only one example.

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Agree with this. It has to be inequalities, I'm pretty sure I've done past papers that agree with this
17. (Original post by Hamburglar)
Agree with this. It has to be inequalities, I'm pretty sure I've done past papers that agree with this
Hi could you help me on the flow question i posted please and arsey solved yesterdays question i had check it out if your still unclear about it .
Thankyou,
Smith
18. (Original post by JayJay95)
I dont think the textbook is incorrect, it doesnt explicitly say that demand and supply have to be met. More specifically it isnt a practical problem. Its been formulated as a linear programming problem and so there is a feesible region in which a range of values can lie up to a maximum. Think about it in real life, when do we ever have a situation where supply meets demand and vice versa?

Im sticking to the textbook on this one, I know the textbook can have mistakes sometimes but this would've been a huge oversight considering theres only one example.
Damn, this has given me something to think about.

Referring still to the textbook example 12 p27 -- you're right, it doesn't specifically say that the demand has to be met. I feel though that, if they don't actually require what they "demand" then they have stated their "demand" incorrectly... if that makes sense.

I mentioned this before, but question 3 in January 2006 allowed either equalities or inequalities - and that was an unbalanced problem in context (transporting fuel from depots to service stations).
19. (Original post by Hamburglar)
Agree with this. It has to be inequalities, I'm pretty sure I've done past papers that agree with this
Which past papers, specifically? I have only seen this type of question come up in January 2006.
20. (Original post by Miken Moose)
Damn, this has given me something to think about.

Referring still to the textbook example 12 p27 -- you're right, it doesn't specifically say that the demand has to be met. I feel though that, if they don't actually require what they "demand" then they have stated their "demand" incorrectly... if that makes sense.

I mentioned this before, but question 3 in January 2006 allowed either equalities or inequalities - and that was an unbalanced problem in context (transporting fuel from depots to service stations).
But the do require that demand. Practically, many companies promise to deliver a certain amount of goods however, unforseen issues occur. Take agriculture as an example. An unforseen drought could occur and destroy half the crop leading to a reduction in supply etc.

In that question I assume they've introduced slack varibles to absorb the excess supply hence the equalities

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