D2 6th June 2013

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

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.

You can do that but thats not the only solution. What you've suggested is the practical solution. Like I said since its a linear programming problem theres a range of values

But it isn't, that's precisely the point. I haven't solved the transportation problem at all, I've just said "Ah to hell with this let's not bother" i.e. don't send anything anywhere. The transportation problem is about selecting how many of which supply points to send to which demand points, whilst still satisfying the demand, to minimise transportation costs. Having those constraints as equations still gives you a feasible region of solutions.

An equation has only one solution. When you use an equal sign instead of an inequality, you dont have a region if solutions, just one. With an inequality you have multiple solutions thats the whole point if linear programming

Er... I agree, "an equation [in one variable] has only one solution". But here there are several equations in several variables. There is more than one solution.

But that's not even the point, anyway. By using inequalities you are ignoring what the transportation problem actually is. The solution where all the decision variables are zero ought to fall out of the feasible region because it doesn't solve the problem.

Perhaps I should draw a simple analogy: say I need to buy several items, A,B,C... and so on, but I want to spend as little money as possible. So I could look at several different shops and what have you and then figure out how to get these items most cheaply from there. What you're saying is that a feasible solution is "don't buy anything" -- well, it's not, because I need those items.

Now, you're probably going to say, "but that's a practical example" -- but it doesn't matter. The point is, you're offering a 'solution' to the wrong problem. The issue of minimising costs in any context can be trivialised by not doing it.

Additionally, the image you posted, which I assume is the practice paper -- I would say that this is more likely to be incorrect than a MS for a genuine D2 paper.

When you have to formulate a maximise Hungarian algorithm as a linear programming problem, why can't you just have the objective function say maximise P=... rather than changing the matrix and doing it as a minimising problem?

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!

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.

Secondly you're trying to find a solution that minimises the cost when theres no need to since they dont ask you for that. All they do is give you a problem, some stock and demand and ask you to formulate it as a LP. They dont say demand meets supply or anything of that kind. They dont say ANYTHING.

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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.

Why do we always work backwards from dynamic programming?

Oh right, well I'm sure you'll be fine! They do include a stupid amount of tables (at least double what it can be done with!)

I know right! I think it's just to make sure I didn't drop it (and not learn the material) so that I didn't have a year without begin forced to learn new material. I don't think they actually want me to get the grade in it though considering I got my A*A* in the other maths A-levels in year 12. Imperial's offer was quite funny! It arrived in like february when I had already got offers from my top two choices and it was A*A*A*A I can remember reading these horror stories in the national papers a year or two ago about a kid who had got an A*A*A* offer and I thought that was mental. And I also read an article about a kid with AAAAA who got rejected by Cambridge but now I realise all this stuff in the paper that they claimed was strange s just normal! There were two kids at my school over the last two years who didn't get in and one got 5A*s and another got 7

Hoping for S's... I have an unfortunate habit of doing worse on the day than I do in mocks though

Fuuck do you think FP2 is easier? Is that needed for Warwick then? (guessed from the fact you're doing STEP I and AEA)

Just did June 2011 btw! Got 70. I remembered "chose the least positive $\theta$ value" incorrectly for the simplex algorithm and picked the largest