OCR (Non MEI) D2 Wednesday 25th May 2016

Isnt it least similar?

Ken should have baked no cakes and got 0 marks for baking and decorating, then difference would have been 0 and he would have won the ridiculous special prize

I am guessing he had to submit a cake, but why not just urinate on it or something. Ensures a double 0

Xsanda’s solutions:

1) Matching
i) JF=3-ND=4
1:MA
2:-
3:JF
4:ND
5:JA
6:MJ
ii) SO=5-JA=2
1:MA 2:JA 3:JF 4:ND 5: SO 6:MJ
iii) 3=JF,4=ND,5=SO always
1:MJ 2:MA 3:JF 4:ND 5: SO 6:JA

2) Flow
i) FT = 2, DT = 4, cut = 9
iia) SCBFT +2 (given)
b) SCFBAEDT +1
iii) 8, with cut {SABCF}{DET} of value 8

3) Hungarian
i) Add dummy column X with 100 in each
Reduce rows -86, -91, -88, -98
Reduce cols -0,-2,-0,-2
ii) AS, BT, CL, no match for D, £271 cost
iii) CS, BT; AL costs £83

4) Rock paper scissors
i) scissors with paper: gain of 1, loss of 2: 1 + (-2) ≠ 0
ii) playsafe: scissors
iii) scissors 2-2p-4q, paper 3p+2q-2, rock 2q-p
iv) p=0.5, q=0.25, rock = 0.25

5) critical path analysis
i) F and H also critical
ii) A: -, B: -, C: -, D: A, E: BD, F: BCD, G: E, H: EF, I: GH, J: H
iii) 60 mins, critical ABDEHJ
iv) allocation for 3 people
v) allocation for 2 people
vi) A is critical, but so is B, which happens at the same time, so must reduce both to gain 5 minutes. 200+400=£600. Best is H and J: £500+£500 = £1000

6i) (0;0)-(1;1)-(2;1)-(3;0)-(4;0): weight 7
ii) 1 point
iii) (0;0)-(1;0) 1
(0;0)-(1;1) 2
(1;0)-(2;0) 1
(1;0)-(2;1) 1
(1;1)-(2;0) 2
(1;1)-(2;1) 1
(2;0)-(3;0) 0
(2;0)-(3;1) 0
(2;1)-(3;0) 2
(2;1)-(3;1) 0
(3;0)-(4;0) 1
(3;1)-(4;0) 2
iv) (0;0)-(1;0)-(2;0)-(3;0)-(4;0): 1 point per round maximum

I don't get how we could have augmented the flow when all the pipes out of the source was full?... or am I mistaken?

I was convinced for most of the paper, that there was a mistake on the flow question, as all the arcs were saturated. You had to reroute a flow of 1, along another route, allowing for an additional flow of 1. You could find a cut of 8 (to prove this was maximal), by highlighting your saturated arcs, and finding the cut which went through only saturated arcs (I forget exactly what it was). It was not a nice question. And that dynamic programming..... Well at least they told me what absolute value means ...

For the first part of the critical path question, if we assume C was critical, does that mean the 2 to follow C were also critical? I wasn't too confident about that one.

Yep, F and H were critical

That is great. When I saw 3 unknowns in the game theory question, I was honestly expecting to be asked to form a simplex tableau...

Xsanda’s solutions:

1) Matching
i) JF=3-ND=4
1:MA
2:-
3:JF
4:ND
5:JA
6:MJ
ii) SO=5-JA=2
1:MA 2:JA 3:JF 4:ND 5: SO 6:MJ
iii) 3=JF,4=ND,5=SO always
1:MJ 2:MA 3:JF 4:ND 5: SO 6:JA

2) Flow
i) FT = 2, DT = 4, cut = 9
iia) SCBFT +2 (given)
b) SCFBAEDT +1
iii) 8, with cut {SABCF}{DET} of value 8

3) Hungarian
i) Add dummy column X with 100 in each
Reduce rows -86, -91, -88, -98
Reduce cols -0,-2,-0,-2
ii) AS, BT, CL, no match for D, £271 cost
iii) CS, BT; AL costs £83

4) Rock paper scissors
i) scissors with paper: gain of 1, loss of 2: 1 + (-2) ≠ 0
ii) playsafe: scissors
iii) scissors 2-2p-4q, paper 3p+2q-2, rock 2q-p
iv) p=0.5, q=0.25, rock = 0.25

5) critical path analysis
i) F and H also critical
ii) A: -, B: -, C: -, D: A, E: BD, F: BCD, G: E, H: EF, I: GH, J: H
iii) 60 mins, critical ABDEHJ
iv) allocation for 3 people
v) allocation for 2 people
vi) A is critical, but so is B, which happens at the same time, so must reduce both to gain 5 minutes. 200+400=£600. Best is H and J: £500+£500 = £1000

6i) (0;0)-(1;1)-(2;1)-(3;0)-(4;0): weight 7
ii) 1 point
iii) (0;0)-(1;0) 1
(0;0)-(1;1) 2
(1;0)-(2;0) 1
(1;0)-(2;1) 1
(1;1)-(2;0) 2
(1;1)-(2;1) 1
(2;0)-(3;0) 0
(2;0)-(3;1) 0
(2;1)-(3;0) 2
(2;1)-(3;1) 0
(3;0)-(4;0) 1
(3;1)-(4;0) 2
iv) (0;0)-(1;0)-(2;0)-(3;0)-(4;0): 1 point per round maximum

soz for spam - how many marks lost for being an idiot and not making the negative values positive for absolute but getting the correct route (and maximin?)??? all the rest of the paper was good :/

I am not an examiner, although I would think you would get the majority of mark if your tabulation is correct (based on your values ) and you got the correct solution + route.

at first i thought negative arc weights was a no no but realised for the MAX(x,y) it's going to always make a positive value so the table wouldn't mess up completely.

Hopefully it is what you say .. fingers crossed because i loved this paper except I'd never heard of absolute before , and they even fcking explained it and I ignored it

That is great. When I saw 3 unknowns in the game theory question, I was honestly expecting to be asked to form a simplex tableau...

for the last question I only put the route but not the minimax value, is that ok?