Apolyton Math Question. bring your calculus hats

[MRT144]

So I asked lord of the mark to not only solve this equation for me but also minimize some factors, and I added some more info to it.

{A/[H/C]}=T

A=(x+((w*L)*(S1+S2+S3+S4+S5))
H=(S1*E1+S2*E2+S3*E3+S4*E4+S5*E5)
C=9/(w(1+E+R+O) and is always rounded up

T=dependent variable, what you're solving for, what you are trying to keep at minimum
x = user defined
w = user defined, whole numbers, try to find equilibrium with s1,s2,s3,s4,s5
L=120
s1,s2,s3,s4,s5 = user defined, whole numbers, try to find equilibrium with w

E, R, O are user defined as either true or false
If E,R,O = true then E,R,O = .5
If E = true then O = False

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

0=< S1 <=8
0=< S2 <=12
0=< S3 <=16
0=< S4 <=20
0=< S5 <=24

this is an equation to find optimal time (T) for producing a given amount (X). With S1 through S5 being the sale type and E1 through E5 being the amount of the sale. The yes or no logical questions relate to sale output increases for E1 through E5.

W are the amount of workers on each sale, and C is how long it takes to make that sale. E, O, R are worker productivity bonuses and increase their productivity by 50% additively. You always round C up to the nearest ones place. 1 worker will produce the the sale in 9 units of time with no bonuses productivity. 2 workers working together will produce a sale in 4.5 turns, but that will be rounded up to 5 units of time with no bonuses to their productivity.

L=the cost of each worker

So what I want to know is how to minimize T to reach X while finding an equilibrium relationship between all the S variables and W as a mathematical function or expression.

I will be going to be in a minute and will be back in around 11 am PST.

[Eli]

[obligatory answer]

42

[/obligatory answer]

[Lul Thyme]

Re: Apolyton Math Question. bring your calculus hats

This is barely readable. Almost none of it makes any sense.

-{A/[H/C]}=T
What is {} and []? are you using them like ()?
Then why didn't you write T=AC/H?

-What does user defined mean?
It's a parameter? A variable?
-What do you mean by find "equilibrium" in this context?

Originally posted by MRT144
If E,R,O = true then E,R,O = .5
If E = true then O = False

How can E,R,O= true if E=true implies O=false?
what about the other cases, say E,R,O=false?

Originally posted by MRT144
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

This is the part that makes the least sense to me.
For example, if E1 and E3 are both true, then E1=90=74?
Also, who cares about the whole true false thing? Why don't you just say that E1 is either 60 or 90? Isn't that simpler?

The last sentence is trivial as far as I can tell.

There are also tons of parentheses used in very awkward ways or missing.

etc...



Basically all the "unknowns" in your equation are "user-defined". If that means that they are given as input, then there are no variables, L is just a constant and there is nothing to minimize.

If they are all variables, and you just want to minimize T, then the range of the variables is too loose and T will not have a minimum and will in fact take any value over the reals.



I strongly suggest you read your post and see if you even understand the question that you are asking.

It's even hard for me to understand what you could mean by "not only solve this equation for me but also minimize some factors".

[MRT144]

Re: Re: Apolyton Math Question. bring your calculus hats

Originally posted by Lul Thyme
This is barely readable. Almost none of it makes any sense.

-{A/[H/C]}=T
What is {} and []? are you using them like ()?
Then why didn't you write T=AC/H?

i was, but I had so many ****ing parenthesis, i couldnt keep it straight.

as for the second part, youre right. I should write it that way. I make that mistake constantly.

-What does user defined mean?
It's a parameter? A variable?
-What do you mean by find "equilibrium" in this context?

it means that the user has to either solve or input it within the ranges given. Some of them have a relationship that isnt defined but i think can be solved for to establish a proportional relationship. for instance I think there is a proportional relationship between s and w but I dont know how to show it and simplify it. I only know basic/intermediate algebra.

How can E,R,O= true if E=true implies O=false?
what about the other cases, say E,R,O=false?

E can be true independent of R being true, but if E is true then O has to be false and vice versa. I guess i messed up the language, but it should be if E = true then E = .5, if R = true then R = .5, if O is true then O=.5, E and O can not be true at the same time. I suppose that O can be discarded.

I guess it was my misuse of commas

This is the part that makes the least sense to me.
For example, if E1 and E3 are both true, then E1=90=74?
Also, who cares about the whole true false thing? Why don't you just say that E1 is either 60 or 90? Isn't that simpler?

well i was trying to explain that if any of E1 through E5 is the higher value for solving, they will all be higher values. if any of E1 through E5 is the lower value, they will all be the lower values.

The last sentence is trivial as far as I can tell.

There are also tons of parentheses used in very awkward ways or missing.

etc...

I know, I am sorry, I really am.

Basically all the "unknowns" in your equation are "user-defined". If that means that they are given as input, then there are no variables, L is just a constant and there is nothing to minimize.

What im looking for though is a way to make sure that T is the smallest possible real number when inputing X S1 through S5 and W and finding the optimal S1 through S5 and W for X and T. Then evaluating several different permutations where E, R, O are true in different regards.

If they are all variables, and you just want to minimize T, I'm pretty sure the range is not strict enough and T will not have a minimum and could, in fact take any value over the reals.

I understand the question, im just not at the level where i can express the question or solve the relation issues of it. Ive been able to solve for T when inputting all the different variables, but I want to be able to establish a function that expresses the constant relationship some of these variables have to one another so that it isnt neccesary for me to input it.

examples of questions I have.

what is the relationship of W and S1 through S5 in making T the smallest number possible.
Does the size of X affect the relationship?
what is the relationship between H and the Sum of S1 through S5?
What is the minimal amount T can be for X when X is >=1?

I apologize again, but I have a lot questions and they arent just the ones above. I want to learn how to do them. I'll try to be more clear in the future.

[KrazyHorse]

WTF does this mean?

w = user defined, whole numbers, try to find equilibrium with s1,s2,s3,s4,s5

[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

E, R, O are user defined as either true or false
If E,R,O = true then E,R,O = .5
If E = true then O = False

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}

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.

[SlowwHand]

MRT! Crapski!

Of all the things to start a thread about, why this?
I almost prefer Oerdin's "Open Wound" thread. Now, that's bad.

[Provost Harrison]

Who let KrazyHorse out of his box?

[KrazyHorse]

Originally posted by Provost Harrison
Who let KrazyHorse out of his box?

What box would that be, son?

[Provost Harrison]

Your box, father.

[KrazyHorse]

Great response.

I'm glad to see that your long-held ability to generate deft witticisms is in no danger of being lost.

[Provost Harrison]

Dumb questions get dumb answers.

[Lawrence of Arabia]

my roomate could answer this question, he was doing stuff like this the last two quarters - too bad hes alseep right now.

[KrazyHorse]

Originally posted by Lawrence of Arabia
my roomate could answer this question

I doubt it, because the problem is not well-posed.

[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.)