D2 6th June 2013

Ahh now i see what you're getting at. You may need thise items but it doesnt mean you're gonna get em since all the stores in your vicinty dont stock them.

...what's that got to do with anything?

Secondly you're trying to find a solution that minimises the cost when theres no need to since they dont ask you for that.

What... I don't even... I can't even understand what you're saying, the transportation problem is minimising transportation costs...

I'm sorry I can't help but feel like you're deliberately ignoring the points I'm making since you're just repeating what you've already said in another guise. Perhaps it's me not making myself clear, I don't know, but I think we should just stop this here. For the record, I will be sticking to what I originally said since no one has actually convinced me that it is wrong. For the third time, in a previous exam question both answers were allowed, anyway.

You know, after all this, it probably won't even come up... :tongue:

So I'll say no more on the subject -- best of luck for tomorrow.

Reply 421

Jkn

11

Original post by Miken Moose

Okay... I've just noticed something glaringly obvious which should settle this. First, this is the solution laid out by example 12 page 27:

Let

Unparseable latex formula:

x_i_j

be the number of units transported from

i

to

j

.

Minimise

Unparseable latex formula:

C = 3x_1_1 + 3x_1_2 + 2x_1_3 + 4x_2_1 + 2x_2_2 + 3x_2_3 + 3x_3_1 + 4x_3_2 + 3x_3_3

Subject to:

Unparseable latex formula:

x_1_1 + x_1_2 + x_1_3 \leq 25

Unparseable latex formula:

x_2_1 + x_2_2 + x_2_3 \leq 40

Unparseable latex formula:

x_3_1 + x_3_2 + x_3_3 \leq 31

Unparseable latex formula:

x_1_1 + x_2_1 + x_3_1 \leq 30

Unparseable latex formula:

x_1_2 + x_2_2 + x_3_2 \leq 30

Unparseable latex formula:

x_1_3 + x_2_3 + x_3_3 \leq 36

Unparseable latex formula:

x_i_j \geq 0

Okay? So, why don't I just set all the

Unparseable latex formula:

x_i_j = 0

? This satisfies all constraints and clearly gives the minimum value of C.

Unless of course, I'm missing something (which for me is quite likely).

I believe is a mistake the book has made which is extremely unfortunate.

I think it should be

Unparseable latex formula:

x_1_1 + x_1_2 + x_1_3 \geq 25

Unparseable latex formula:

x_2_1 + x_2_2 + x_2_3 \geq 40

Unparseable latex formula:

x_3_1 + x_3_2 + x_3_3 \geq 31

Unparseable latex formula:

x_1_1 + x_2_1 + x_3_1 \geq 30

Unparseable latex formula:

x_1_2 + x_2_2 + x_3_2 \geq 30

Unparseable latex formula:

x_1_3 + x_2_3 + x_3_3 \geq 36

so that there is conflict between the constraints and objective function in such a way that the tableaux has a stable state (a solution) when all slack variables are equal to zero. :tongue:

Reply 422

Miken Moose

3

Eh? Okay, I know I said I was going to leave this but... A cannot supply more than 25...?

Reply 423

lanky

In GT LP, whats the difference between writing the constraints as equalities or writing them as equations?

(edited 10 years ago)

Reply 424

JayJay95

Original post by Miken Moose

Yes, but that has no effect on the solution that I developed theoretically and independently beforehand?
No -- they allowed equalities or inequalities for the demand totals (i.e. columns), but they only allowed inequalities for the supply totals (i.e. rows). This reflects what I originally said.

I checked that paper and mark scheme but it looks like someone wrote that mark scheme themselves where it says you could use equalities. I remember doing that question and I managed to find it on practice paper b

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Reply 425

RYRK

2

Original post by Jkn

I believe is a mistake the book has made which is extremely unfortunate.

I think it should be

Unparseable latex formula:

x_1_1 + x_1_2 + x_1_3 \geq 25

Unparseable latex formula:

x_2_1 + x_2_2 + x_2_3 \geq 40

Unparseable latex formula:

x_3_1 + x_3_2 + x_3_3 \geq 31

Unparseable latex formula:

x_1_1 + x_2_1 + x_3_1 \geq 30

Unparseable latex formula:

x_1_2 + x_2_2 + x_3_2 \geq 30

Unparseable latex formula:

x_1_3 + x_2_3 + x_3_3 \geq 36

so that there is conflict between the constraints and objective function in such a way that the tableaux has a stable state (a solution) when all slack variables are equal to zero. :tongue:

it should be less than or equal to , you cant have more stock than there is , so it has to be less or equal to, correct me if i am wrong :smile:

.

Reply 426

Jkn

11

Original post by Miken Moose

Eh? Okay, I know I said I was going to leave this but... A cannot supply more than 25...?

Well yes but you are generalising so that you can apply the method before degeneralising afterwards. The solution, in this case, should drift towards the special case of this generalisation (equality on all major constraints) and hence eliminate the need for the degeneralisation after using the tableaux. What the slack variables do is to enable useful algebraic manipulation.

I think this is right... does anyone else want to jump in?

The technique of generalising in order to apply a process is often very useful in mathematics. For example, with integration, you learn the Leibniz integral rule ("differentiation under the integral sign") which basically assigns a second variable to the function you are looking to integrate in order to enable you to take a partial derivative of the integral as a whole with respect to the new variable followed by successive integration of the new function with respect to each variable in turn. This is very useful in simplifying otherwise awkward problems and was favourite of Richard Feynman :tongue:

Original post by brittanna

I didn't even get an Imperial offer :grumble:

(or a Cambridge one, but after my interview i'm really not surprised), and when I asked them why, they said 'we take a wide range of factors into consideration when making offers, please check our entry requirements page for more information' I really wasn't very impressed :colonhash:

. I'm hoping for a 1 in STEP I, but I won't be disappointed if I only get a 2. I want a distinction in AEA, but if a vectors question comes up (I have no idea how are you supposed to see half of the things they expect you to see!), then I won't be expecting much from it :tongue:

.

I wouldn't say I think FP2 is easier, it's just that I tend do worse on the applied modules than on the pure modules, and so i'm probably more likely to lose fewer marks on FP2. And yeah, that's for Warwick.

I'm not trying to show of or anything, but I just did practice paper A and got 75 :cool:

. Although yesterday I did june 2010 and got about 65 :colondollar:

(this was mainly due to looking at the wrong tables when doing the transportation one :colonhash:

).

Aren't they supposed to give detailed feedback to your school afterwards? :eek:

What college did you apply to btw?

Well good luck! I'm sure you'll destroy it! **** vectors... I avoid them like the plague... Ah, they are my insurance! :biggrin:

Visited there 3 times (open day then STEP courses), seems a great department!

Nice one! I'm restricting myself to the new ones given that I have 13 exams in total :lol:

Hmm you just need to find ways to do loads of checks. Like thinking about the constraints of your values (should be integers!) and remarking that the shadow costs must have exactly one degree of freedom :tongue:

Reply 427

JayJay95

Original post by Miken Moose

...what's that got to do with anything?

What... I don't even... I can't even understand what you're saying, the transportation problem is minimising transportation costs...

I'm sorry I can't help but feel like you're deliberately ignoring the points I'm making since you're just repeating what you've already said in another guise. Perhaps it's me not making myself clear, I don't know, but I think we should just stop this here. For the record, I will be sticking to what I originally said since no one has actually convinced me that it is wrong. For the third time, in a previous exam question both answers were allowed, anyway.

You know, after all this, it probably won't even come up... :tongue:

So I'll say no more on the subject -- best of luck for tomorrow.

Yeah im not perfect at this either and you're right i doubt itll come up. Been in zombie mode for the past few days revising lol sorry if i dont make sense.

Hope all goes well tomorrow :smile:

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Reply 428

TheGuy117

14

Can someone explain part c please? :smile:

Reply 429

BobLoblawLawBlog

16

Original post by Jkn

Well yes but you are generalising so that you can apply the method before degeneralising afterwards. The solution, in this case, should drift towards the special case of this generalisation (equality on all major constraints) and hence eliminate the need for the degeneralisation after using the tableaux. What the slack variables do is to enable useful algebraic manipulation.

I think this is right... does anyone else want to jump in?

The technique of generalising in order to apply a process is often very useful in mathematics. For example, with integration, you learn the Leibniz integral rule ("differentiation under the integral sign") which basically assigns a second variable to the function you are looking to integrate in order to enable you to take a partial derivative of the integral as a whole with respect to the new variable followed by successive integration of the new function with respect to each variable in turn. This is very useful in simplifying otherwise awkward problems and was favourite of Richard Feynman :tongue:

Aren't they supposed to give detailed feedback to your school afterwards? :eek:

What college did you apply to btw?

Well good luck! I'm sure you'll destroy it! **** vectors... I avoid them like the plague... Ah, they are my insurance! :biggrin:

Visited there 3 times (open day then STEP courses), seems a great department!

Nice one! I'm restricting myself to the new ones given that I have 13 exams in total :lol:

Hmm you just need to find ways to do loads of checks. Like thinking about the constraints of your values (should be integers!) and remarking that the shadow costs must have exactly one degree of freedom :tongue:

I didn't request any feedback from Cambridge (as I know it was due to how badly my interview went), it was just Imperials general comment that annoyed me (I still have no idea why I was rejected). I applied to Selwyn, it was so nice there :rolleyes:

, but Warwick is really nice as well, so i'll be really happy if I get in.

I only have 7 exams, but 5 of them are maths (C4, FP2, D2, STEP I, AEA). The others are chemistry and physics so I have a bit more time haha.

If I have any time left at the end, I could try a few trial and error routes/ allocations as well :colondollar:

. Depending on the no. tables I have left, I could also redo some of the questions :cool:

.

Which college did you apply to? I'm going to guess at Pembroke?

Reply 430

Arsey

10

Original post by TheGuy117

Can someone explain part c please? :smile:

you need to think about the stage that takes the longest as the overall time is dictated to by this. So work out the time taken to get all done by that stage then add the quickest times of the remaining processes

Reply 431

Arsey

10

Original post by lanky

In GT LP, whats the difference between writing the constraints as equalities or writing them as equations?

depends on what is asked, a general GT LP question will always take the form

v - aP1 - bP2 - cP3 <= 0 etc

it may asks for equations to be used in a simplex tableau, to do this add a slack variable and make = 0

Reply 432

BobLoblawLawBlog

16

Original post by Arsey

depends on what is asked, a general GT LP question will always take the form

v - aP1 - bP2 - cP3 <= 0 etc

it may asks for equations to be used in a simplex tableau, to do this add a slack variable and make = 0

For Transportation linear programming problems (balanced), do we use equalities or inequalities?

Reply 433

Arsey

10

Original post by Jkn

I believe is a mistake the book has made which is extremely unfortunate.

I think it should be

Unparseable latex formula:

x_1_1 + x_1_2 + x_1_3 \geq 25

Unparseable latex formula:

x_2_1 + x_2_2 + x_2_3 \geq 40

Unparseable latex formula:

x_3_1 + x_3_2 + x_3_3 \geq 31

Unparseable latex formula:

x_1_1 + x_2_1 + x_3_1 \geq 30

Unparseable latex formula:

x_1_2 + x_2_2 + x_3_2 \geq 30

Unparseable latex formula:

x_1_3 + x_2_3 + x_3_3 \geq 36

so that there is conflict between the constraints and objective function in such a way that the tableaux has a stable state (a solution) when all slack variables are equal to zero. :tongue:

nooooo

it is definitely <=

you cannot deliver more than the demand.
you cannot deliver more than what is available in stock.

Also, not all of Xij can be zero, otherwise you are delivering nothing from everywhere to everyone....

Reply 434

Arsey

10

Original post by brittanna

For Transportation linear programming problems (balanced), do we use equalities or inequalities?

well technically = as you will deliver all your stock to meet the demand.

However, you will get away with <= on all transportation questions.

Reply 435

Jkn

11

Original post by RYRK

it should be less than or equal to , you cant have more stock than there is , so it has to be less or equal to, correct me if i am wrong :smile:

.

Well you could just put the slack variable on the other side :tongue:

Tbf they probably won't pull this question on us! And if they do we can just copy the book because, even if it is wrong, they would have to allow answers that copied it if any teachers wrote emails to them after the exam pointing out the error :smile:

Original post by brittanna

I didn't request any feedback from Cambridge (as I know it was due to how badly my interview went), it was just Imperials general comment that annoyed me (I still have no idea why I was rejected). I applied to Selwyn, it was so nice there :rolleyes:

, but Warwick is really nice as well, so i'll be really happy if I get in.

I only have 7 exams, but 5 of them are maths (C4, FP2, D2, STEP I, AEA). The others are chemistry and physics so I have a bit more time haha.

If I have any time left at the end, I could try a few trial and error routes/ allocations as well :colondollar:

. Depending on the no. tables I have left, I could also redo some of the questions :cool:

.

Which college did you apply to? I'm going to guess at Pembroke?

What happened in the interview? I was under so much pressure in mine I nearly dropped dead! Hmm Imperial are such pricks, they seem so cold and distant, with their late replies and template responses... though perhaps they are just playing hard to get :wink:

hahahaha!

Physics next thursday (OCR)? I really need to start revising it... :eek:

Why would you want to do that? :tongue:

And redoing questions would probably be detrimental... if you have extra time either check for errors or write a funny note to the examiner :tongue:

Why do you think Pembroke? :lol:

That's where LOTF and DJ Mayes have offers but that is largely coincidental (though it is one of the few most academic and prestigious colleges). The most prestigious college for maths is Trinity and the one with the best results across the board (year-by-year average) is Emmanuel. I have my offer from Emmanuel :wink:

mwuhahaha

Reply 436

Arsey

10

Original post by ChelseaSam

In travelling salesman.. If the network is not complete... as in the n vertices are not connected to every other vertex - do we have to create a table of least distances in order to use the NN algorithm and prims etc etc or do we use the network we are given? Thanks!

Unless it specifies to use a table, use the network. I generally find it quicker, just be careful of sneakies.

Using the graph will also give the proper tour when doing NN

Reply 437

BobLoblawLawBlog

16

Original post by Jkn

Well you could just put the slack variable on the other side :tongue:

Tbf they probably won't pull this question on us! And if they do we can just copy the book because, even if it is wrong, they would have to allow answers that copied it if any teachers wrote emails to them after the exam pointing out the error :smile:

What happened in the interview? I was under so much pressure in mine I nearly dropped dead! Hmm Imperial are such pricks, they seem so cold and distant, with their late replies and template responses... though perhaps they are just playing hard to get :wink:

hahahaha!

Physics next thursday (OCR)? I really need to start revising it... :eek:

Why would you want to do that? :tongue:

And redoing questions would probably be detrimental... if you have extra time either check for errors or write a funny note to the examiner :tongue:

Why do you think Pembroke? :lol:

That's where LOTF and DJ Mayes have offers but that is largely coincidental (though it is one of the few most academic and prestigious colleges). The most prestigious college for maths is Trinity and the one with the best results across the board (year-by-year average) is Emmanuel. I have my offer from Emmanuel :wink:

mwuhahaha

I just really wasn't very good at maths, I got some questions wrong that I really shouldn't have! But I think I've improved a lot since I've started looking at STEP.

I have edexcel physics :s-smilie:

. At least this exam is nicer than unit 4 for us (no more maganetic and electric fields or electricity). The problem is that I feel as though I know the content, I just can't answer the exam questions :lol:

.

I just guessed Pembroke as there were quite a few people that applied there this year :tongue:

. Well done on getting an offer from the (maybe second best at most) college :colone:

.

Reply 438

RYRK

2

ok , i got a quick question, when writing a maximizing allocation problem as a linear progamming problem, u first transform the matrix and then continue as normal, so would the objective be to maximise or minimise, i looked on the example of the book on page 55 , and this one is minimising and i am not sure it it is right?