Apolyton Math Question. bring your calculus hats

[Lul Thyme]

Originally posted by Lawrence of Arabia
dont doubt it, theres people smarter than you out there, and hes studied this stuff. hes studied this stuff and knows what they are asking, so even if its poorly worded, you can still figure out whats going on (variables are the same, etc.)

That doesn't really make sense.
It's not about being smart or having studied this stuff.
If a question is not well posed, there is no definite answer.

It's not about mathematics any more, it's about deciding what question you're going to make up to replace the one posed.

To give a dumb example, it a bit like me asking "minimize f(2+=b while looking for the equilibrium of b where true is 3(" which of course doesn't mean anything.

It's not about being smarter than Krazyhorse, there just isn't an answer.
Somebody could assume that he meant A, and deduce a certain answer and somebody else could assume the question meant B and deduce a different answer.

Even if one DOES in fact guess correctly what the person asking the question meant, from a mathematical point of view he's not any more right (or wrong).



If you don't agree, I'll gladly wait for your roommate to wake up and answer. I'm in no hurry and I doubt MRT's life is hanging on the line either.

[KrazyHorse]

Originally posted by Lawrence of Arabia
dont doubt it, theres people smarter than you out there, and hes studied this stuff. hes studied this stuff and knows what they are asking, so even if its poorly worded, you can still figure out whats going on (variables are the same, etc.)

This would be more true if the question wasn't so detailed. I can answer even badly posed physics questions, but only if they're simple, standard ones.

When you have 20 different named variables+parameters and what's obviously a whole host of assumptions then it becomes vanishingly likely that your roommate has any more clue what MRT's asking than anybody else.

[MRT144]

[QUOTE] Originally posted by KrazyHorse
Also, which are your parameters and which are your variables. I can't tell.

and this part

E1, E2, E3, E4, E4 are user defined as either true or false
If E1 = true then E1 = 90, false = 60
If E2 = true then E1 = 90, false = 60
If E3 = true then E1 = 74, false = 50
If E4 = true then E1 = 60, false = 40
If E5 = true then E1 =44, false = 30
If E1,E2,E3,E4,E5 = true then E1 through E5 = true

makes no sense

[quote/]

youre right, disregard that part and refer to the post furhter down

What the hell does this mean? Why don't you simply replace E+R+O with a quantity Z which is restricted to {0, 0.5, 1}

good idea.

it means that the user has to either solve or input it within the ranges given

Which one is it? Are we minimizing with respect to these, or are they parameters defined by some external relationship you're not telling us?

Why don't you simply give us the real problem instead of your badly-distilled version of it? As far as I can tell this is a simple, though tedious problem.

okay, ill define some things further. The thing is KH, Im making this problem up, but dont know the language to translate it well enough for you guys.

9/w(1+1)*(10000+(s1+s2+s3+s4+s5)*W*120)/(s1*E1+s2*E2+s3*E3+s4*E4+s5*E5)=T
9/w(1+1)*(10000+(s1+s2+s3+s4+s5)*W*120)/(s1*90+s2*90+s3*74+s4*60+s5*44)=T

I defined Z as 1 for this example. In another example it could be .5, or it could be 0. In this example it is 1.

what the smallest number T can be when s1=<8, s2=<12, s3=<16, s4=<20, s5=<24 and are all whole numbers.

ill leave it at that for now and get back to you.

[KrazyHorse]

Dude, it's important for you to tell us if w is fixed!!!

Can we change it to minimise T, or not?

[KrazyHorse]

Also, why is there now a small w and a big W?

[Lul Thyme]

Originally posted by MRT144


9/w(1+1)*(10000+(s1+s2+s3+s4+s5)*W*120)/(s1*90+s2*90+s3*74+s4*60+s5*44)=T


what the smallest number T can be when s1=<8, s2=<12, s3=<16, s4=<20, s5=<24

Ok I'm assuming w=W.

T=9/w(1+1)*(10000+(s1+s2+s3+s4+s5)*w*120)/(s1*90+s2*90+s3*74+s4*60+s5*44)
=9(90s1+90s2+74s3+60s4+44s5)/(20000w+240w^2(s1+s2+s3+s4+s5))


Let A=9(90s1+90s2+74s3+60s4+44s5), B=20000, C=240(s1+s2+s3+s4+s5)

At this point I'm assuming that w is the variable with respect to which we are optimizing, since you never really made this clear (and s1, s2, s3, s4, s5 are parameters).


So T(w)=A/(Bw+Cw^2)
If A=0 then T(w)=0.
If A>0, then
lim T(w) as w->0- is -infinity.
If A<0, then
lim T(w) as w->0+ is -infinity.
In both those cases, there is no minimum.



So that answers THAT question, although I still have no idea if that was it.

[KrazyHorse]

I think we're actually minimising with respect to S1,...,S5

[KrazyHorse]

(those quantities taking on only integer values)

[Lul Thyme]

Originally posted by KrazyHorse
I think we're actually minimising with respect to S1,...,S5

Could be.
But then what's w?
In any case, from looking quickly at it, it would seem there is also no minimum if those are the variables, unless many more restriction added.
There are so many possibilities...
We have to wait for LoA's roommate to read MRT's mind I guess

[Lul Thyme]

Anyway MRT to get back to the point, you have to understand the difference between a variable and a parameter in an optimization problem.
Let's take an easy example.
Let T=x^2+a.
I want to "minimize T WITH RESPECT TO x".
That means that x is a variable, and a is assumed to be a parameter.
In this case the minimum is at x=0, and the value for T at x=0 is a.

This is very different than asking to "minimize T WITH RESPECT TO a" which has no solution because as a gets smaller, so does T.

So there are many different optimization problems from the same equation, and you have to be very clear what you're asking.

This is very informal:
What are the "unknowns" that are actually "known" that is they vary from problem to problem, but for a specific problem, they are constants.
Those are parameters.

The "unknowns" which make the function vary in an actual problem are the variables.

More or less.

[KrazyHorse]

If he wants us to minimise wrt S1,...,S5 then I hope he realises that the minimum always occurs with all 5 quantities at one or the other of each of their endpoints...

[Lul Thyme]

Originally posted by KrazyHorse
If he wants us to minimise wrt S1,...,S5 then I hope he realises that the minimum always occurs with all 5 quantities at one or the other of each of their endpoints...

That's probably true although it's not immediate for me(is that automatic for a quotient of linear functions?).
In any case, there's only one bound which is why T is unbounded. (all this if w is a parameter, I don't know what else it could be in this perspective.)

[KrazyHorse]

Originally posted by Lul Thyme

That's probably true although it's not immediate

Yes it is.

The derivative wrt Si has no zeroes at finite Si

[KrazyHorse]

Originally posted by Lul Thyme
is that automatic for a quotient of linear functions?

Yes, of course. d((a1+b1x)/(a2+b2x))/dx = (b1a2-a1b2)/(a2+b2x)^2

[Lul Thyme]

Originally posted by KrazyHorse


Yes, of course. d((a1+b1x)/(a2+b2x))/dx = (b1a2-a1b2)/(a2+b2x)^2

Yes, I knew it worked in one variable but never asked myself if it would in many.



EDIT:
I guess it does.
The partial derivatives have to be 0 so almost the same argument goes through.