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# D2 6th June 2013 Watch

1. (Original post by NiceToMeetYou)
Could you explain how to read the summation notation? I haven't a clue how it works/how to read it and as a result am reluctant to read it (don't have a teacher to ask either)
It is quite difficult to explain without demonstration. Have you done summation in FP1 yet?

i represents the rows; say 1, 2, 3

j represents the columns; say A, B, C

so in an allocation problem you know the sum of the first row (and every other row) is equal to 1

rather than writing X1A + X1B + X1C = 1

you could write SUM X1j = 1'

same thing for transportation questions, except ALWAYS use <=
2. (Original post by Arsey)
no, you do not. I think if the question was asked 90% of candidates would answer it that way.

You have to answer it as you would a normal Max allocation question.

You first subtract every element from the largest value in the table. Next, you answer it as every other LP minimising question.
Ahhh, oh yeah, I actually made a note of that. Is there a reason maximising P = etc. wouldn't work?
3. Could anyone help me on the flow questions posted please
Thanks,
Smith
4. (Original post by smith50)
I don't understand these two questions could you help please:
Attachment 223341
Attachment 223343

P.S - How do you know which are can be increased in flow ?

Thanks,
Smith

part f) is just common sense, using the conservation condition.

Look at each.

It is pointless increasing DH since you already have a capacity of 26 flowing into H but only 25 can leave H.

You could only increase CF by 1, since you have a capacity of 15 flowing into F and only 16 can leave F

BE is the way to go since you only have a capacity of 12 flowing into E but you have a capacity of 24 out of E, so just looking at E, you could increase the capacity of BE by 12.
5. (Original post by knowledgecorruptz)
Ahhh, oh yeah, I actually made a note of that. Is there a reason maximising P = etc. wouldn't work?
ju

Just think about what you are trying to do. You are trying to allocate workers to tasks. So unless you turn it into a min problem the Hungarian algo will not work, so when forming the LP you must do this, otherwise it will not be solved.
6. (Original post by smith50)
Could anyone help me on the flow questions posted please
Thanks,
Smith
what part of the second flows question do you not understand
7. (Original post by Arsey)
It is quite difficult to explain without demonstration. Have you done summation in FP1 yet?

i represents the rows; say 1, 2, 3

j represents the columns; say A, B, C

so in an allocation problem you know the sum of the first row (and every other row) is equal to 1

rather than writing X1A + X1B + X1C = 1

you could write SUM X1j = 1'

same thing for transportation questions, except ALWAYS use <=
I've done FP1 and understand summations and what they do etc, it was the i,j bit I'm confused about but I think I get it now thanks

So is SUM X1j = 1 saying
Sum all the elements of j in row 1 and they equal 1?

So if we wanted to find the sum of column A it would be
SUM XiA = 1?

Thanks again
8. (Original post by Arsey)
what part of the second flows question do you not understand
I kinda understand part c and d but not fully could you help please.
Thankyou,
Smith
9. May 2012, Question 6, Part C
As you're finding your routes from the diagram in part B, I prefer to cross out the numbers to put new flows on but part b was to fill some of these in and the flow augmentating (no idea how to spell) route involves crossing some of these out

In the exam as long as I left them legible, would that be ok do you think?
10. (Original post by NiceToMeetYou)
I've done FP1 and understand summations and what they do etc, it was the i,j bit I'm confused about but I think I get it now thanks

So is SUM X1j = 1 saying
Sum all the elements of j in row 1 and they equal 1?

So if we wanted to find the sum of column A it would be
SUM XiA = 1?

Thanks again
spot on. Once you get the hang of it, this question is gift marks.
11. (Original post by NiceToMeetYou)
May 2012, Question 6, Part C
As you're finding your routes from the diagram in part B, I prefer to cross out the numbers to put new flows on but part b was to fill some of these in and the flow augmentating (no idea how to spell) route involves crossing some of these out

In the exam as long as I left them legible, would that be ok do you think?
I wouldn't cross anything out, do it as it says in the textbook.

I share your worry though, I have no idea how to present these flow diagrams. It just turns into a giant mess :s
12. JUNE 2009 4A - is the mark scheme wrong for the cut value for C2?
Value of C2 by the MS is 45 - any ideas?
13. (Original post by sacheeen)
JUNE 2009 4A - is the mark scheme wrong for the cut value for C2?
Value of C2 by the MS is 45 - any ideas?
(Original post by Arsey)
spot on. Once you get the hang of it, this question is gift marks.
Hi, is the mark scheme value for this cut wrong? C2 given by the mark scheme is 45 but I found a value of 42. Any ideas?
14. (Original post by Hamburglar)
I wouldn't cross anything out, do it as it says in the textbook.

I share your worry though, I have no idea how to present these flow diagrams. It just turns into a giant mess :s
I swear the textbook uses multiple diagrams/says relabel the diagram which doesn't seem to be an option in the exam answer book
15. (Original post by sacheeen)
JUNE 2009 4A - is the mark scheme wrong for the cut value for C2?
Value of C2 by the MS is 45 - any ideas?
That's right it's 7+5+8+25=45 don't use the arrows out of the cut
Smith
16. (Original post by sacheeen)
JUNE 2009 4A - is the mark scheme wrong for the cut value for C2?
Value of C2 by the MS is 45 - any ideas?
Looks like 45 to me.

ET, DF, BF, GT

7 + 5 + 8 + 25 = 45
17. (Original post by NiceToMeetYou)
I swear the textbook uses multiple diagrams/says relabel the diagram which doesn't seem to be an option in the exam answer book
Yeah it might do. The question sort of implies that you use the current diagram for the labelling procedure though :s It looks a mess
18. (Original post by Hamburglar)
I wouldn't cross anything out, do it as it says in the textbook.

I share your worry though, I have no idea how to present these flow diagrams. It just turns into a giant mess :s
Wait, how would you do it without crossing anything out?
19. (Original post by Hamburglar)
Yeah it might do. The question sort of implies that you use the current diagram for the labelling procedure though :s It looks a mess
The markscheme just states the 2 routes used, and with part D wanting you to label a flow digram showing the max flow I don't know how you're expected to do it all in your head
It really is a mess
20. (Original post by smith50)
I kinda understand part c and d but not fully could you help please.
Thankyou,
Smith
If one of those cuts is a min cut, then the max flow must be the smaller of the two.

Just looking at it, C1 is 40, so that is the max flow.

you need to look at the flow pattern, again using the conservation condition.

the total capacity into F is 16 which means the max flow of FG is also 16, this in turn means the max flow into G is 24 meaning the max flow of GT is 24.

The max capacity into H is 16, so the max flow of HT is also 16.

Given that we know max flow is 40, then GT has to be 24.

d)
The max capacity into D is 24 but only 21 can leave from D, this means the max flow into is also 21.

AC has to be 8 otherwise the max flow is impossible. So the maximum flow of AD is 12.

If AD is 12, DB has to be 9 (to make 21) but DB could be 10 meaning that AD could also be 11 (to make 21). So AD must be 11 or 12.

This in turn means that SA must be 19 or 20.

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