QMA finals help please (1 Viewer)

[angelfromabuv]

Hey guys i need a bit of direction with a couple QMA questoins if anyones up for it.
First is the whole Ax=B thing,
We were trying to find a local maximum, (i.e. fx=fy=0)
We have:

fx= -2(x-1)
fy= -2 (y-1)
Then solve for any (x,y) that satisfy fx=fy=0

Then we had to solve with the matrix thing, and the correct matrix is
|2 0| 2|
|0 2| 2|

The 2, 0, 0, 2 is the A matrix, then the [2, 2] is the solution matrix but i don't understand how htey got that? It was something about 2 of x + 0 of y=2 but... :S


2nd question is about '06 finals paper
-1. For Q3 how do we find the Iso-objective line? Do we just stick in any point and solve?

-2. (e) Down to what level of investment will the change you found in (d) for every decrease of one dollar apply? -->What does this even mean?

-3. What's the deal with the Hessian matrix thing? Coz its a fair blurr to me :S!

I know that sounds like a lot sorry but any nudge in teh right direction is much appreciated thanks!

 

[shinji]

For the first question, i don't really understand the context of it. Would you be able to provide a reference to the actual question?

2nd questions;
- 1
Yeah, to find the Iso-objective line yuo would just plug in any number to be the revenue. Then you would make Y equal to something and then solve for x. and then graph.

-2 Basically, saying as you decrease $1 of investment, how much would maximum return change. What you found in (d), (decrease in $1 -> decrease in max. return of 6cents), up to what point would this be applicable?
I.e, you would have to refer to you graph that you drew.

-3. : hessian matrix. i don't think we've learnt it, but i did some research on it and did the question now i can't find it. lol

 

[Loz_metalhead]

We learn't the hessian matrix and its pretty important

Have a look over the lecture notes. The hessian matrix is the second order condition for questions with a constraint-it will tell you if its a minimum and maximum. gx is the derivative of x in the constraint, gy is the derivative of the y in the constraint.

Lxx-its just d2y/dx2
Lxy-d2y/dxdy

 

[angelfromabuv]

Ah ur a champ thanks heaps. Which lecturer do u have? QMA not my fave subject haha, i got Fox, i feel bad for him tho coz everyone likes Angus. That thing was from Lecture 24, if it's too much trouble dw bout it. I just have no idea how htey got the solutions vector as [2, 2] for example 24.2.

Goodluck tomorow! doesn't sound like u need it tho
haha fingers crossed we don't get any of that hessian stuff watever it is

 

[Chris.]

hoping to get 30/60

is the exam out of 60 marks?

 

[shinji]

hoping to get 30/60

is the exam out of 60 marks?

65 marks

But in reply to the first question, i know how they get it i think.

That's essentially plotting the function of the first partial derivatives into a matrix.
it's in the form;

F_x = -2x + 2
F_y = -2y + 2

to obtain the maxima of things, we would normally set the derivative equal to zero.
I.e, -2x + 2 = 0
-2y + 2 = 0

Then, u just move the 2's over to the other side,
so it becomes
2x + 0 = 2
0 + 2y = 2
(note, in a matrix, the first column would correspon to the "x" variable, 2nd column would be "Y" variable, etc)

and then remove the variables and then put it into matrix form ='s

|2 0|2|
|0 2|2|

hope you understood that.

 

[Casmira]

its out of 60 (10 marks 6 questions)

 

[angelfromabuv]

hey shinji that helps a lot thank u! much clearer now on the slim chance that u may need my help lol i'll be around if u need anything as well, thanks!

 

[shinji]

hey shinji that helps a lot thank u! much clearer now on the slim chance that u may need my help lol i'll be around if u need anything as well, thanks!

Well if you could kindly explain Lagrange Multiplier method for me, i'd be forever greatful!

haha.
i kinda..skippedthat lecture. ^^"

 

[Chris.]

Well if you could kindly explain Lagrange Multiplier method for me, i'd be forever greatful!

haha.
i kinda..skippedthat lecture. ^^"

i just learnt that shit man dont mention it lol

i need 25/60 to pass, and i dont even know if i can achieve that. the weather sucks ass too. hoping to gain the majority of marks from annuities, matrices, linear programming and marks here and there from calculus.

 

[angelfromabuv]

Lagrange Multiplier? aahh that things a bit messy and i think i just got the hang of it, i think the best way i can explain it is to go thru the '06 question number 5? if that helps here we go:

The lagrange format is on the formula sheet, so for the f(x,y) bit that we've found from teh sectoin above--> L= (what you want to maximise) + lambda (constraint)

We insert functions given so that gives you:

L= 240x -[FONT=CMBX12~18]x^2[/FONT] + [FONT=CMBX12~18]140y -[/FONT] [FONT=CMBX12~18]y^2[/FONT] - [FONT=CMBX12~18]200 [/FONT]+ lambda [(80-(x + y)]
The last bit after lambda is the cost function which is our constraint (i get a bit confused as to what happened to teh 10 in front of teh 10(x + y) and wateva but yea...)

AFter that you do the partial differentiation for x, y and lambda, then set taht all = 0
Lx=0
Ly=0
L(lambda)=0

Then solve both your x and y for lambda, so now they both equal lambda, they equal each other i.e. (240-2x=140-2y)
Solve for y
Sub Y into the L(lambda)=0 equation and solve for Y
Now you have x and Y, then sub both of these into either the Lx=0 or the Ly=0 to find lambda,
Then sub all of these (x, y, lambda) into the initial profit equation to find your profit.

And then we have to check for a max using teh Hessian....and this is where i'm up to lol
does that make any sense? hope it helps a tad!

Did anyone get that Hessian question in Quiz 4? had me completely stumped no idea how to do it :S
sub

 

[angelfromabuv]

um someone might wana check i'm doing all the right thigns yea? i have trouble figuring out how to put in teh constraints...any tips :S?

 

[Lavenderpup]

in quiz four, you use the small hessian to check which is fxxfyy - fxy^2 aka it's determinant gets used and if its >0 then its a max, and if its <0 then its a min.

and with lagrangian you use the bigger hessian as indicated by its g and Ls.
.. well that's how I remember that anyway :/

 

[shinji]

Wow. thanks for that angelfromabuv!!

Also just to check, we can also use Matrices to solve the L_x=L_y=L_lambda=0 yeah?