Lagrange multipliers Definition and 179 Threads

(1) f(x,y,z)=x+2y (2) x+y+z=1 (3) y^2+z^2=4 1=\lambda 2=\lambda+2y\mu 0=\lambda+2z\mu u=\frac{1}{2y} y=\pm\sqrt2 \ \ \ z=\pm\sqrt2 Plugging into equation 2 to solve for x. How do I know to use either y=\sqrt 2 \ \mbox{or} \ y=-\sqrt2 ... similarly with my values for z. edit: NVM, I'm an...

Homework Statement The Park Service is building shelters for hikers along the Appalachian Trail. Each shelter has a back, a top, and two sides. Find the dimensions that will maximize the volume while using 384 square feet of wood. They want me to find the length, width, and height...

I'm having a little trouble with another old test question. It states: Use LaGrange multipliers to find the point on the line 2x + 3y = 3 that is closest to the point P(4, 2). I assume that my constraint is g(x, y) = 2x + 3y = 3, and I have to come up with a function f(x, y) to be...

Homework Statement A uniform hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R. The only external force is that of gravity. If the smaller cylinder starts rolling from rest on top of the bigger cylinder , use the method of lagrange multipliers to find the point...

Hi! I've been studying Dirac's programme for some time and I realized that there's something missing: Actually this is missing in every standard book on classical mechanics concerning how constraints are implemented in the lagrangian. They are usually inserted with some unknown variables...

hi, i just learned about lagrange multipliers and i am very confused about how to derive and use them. another thing, how would you use them to find points on a surface that are closest to a given point outside the surface

Homework Statement find the max and min of f(x,y)=x^2y, constraint x^2+y^2=1 Homework Equations None. The Attempt at a Solution I found that possible points use the procedure of the method of lagrange multiplier, I got (\pm\sqrt{2/3}, \pm\sqrt{1/3} so 4 points total. But do I have to...

Hello, I was hoping someone would be able to clarify a problem I've got. A lagrange multiplier can be introduced into an action to impose a constraint right? I was wondering what relation lagrange multipliers have to gauge conditions, which are imposed by hand. Am I correct in saying that...

Homework Statement Find the maximum x1, x2, x3, in the ellipsoid x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1 and all the places where this value is attained.Homework Equations The Attempt at a Solution My teacher said to use the lagrange multiplier. So far, I have that we are maximizing x1, x2, and x3...

I've just started multi dimensional calculus, among which Langrange's Multipliers. I have some questions which will help me grasp the concepts since I'm a very curious guy... a) What are you finding exactly with this technique? b) What is the constraint? c) What does the extra variable...

My math is a little rusty and I want someone to identify the category of problem (Lagrange Multipliers, Simplex method, ...) I have, so that I can read up on the topic and familiarize myself with the technique. To make the problem simple, let's say I have some number of chips of varying...

Hey, I need help with a problem involving Lagrange multipliers... Here is the question: Find the absolute maximum and minimum of the function f(x,y) = x^2-y^2 subject to the constraint x^2+y^2=289. As usual, ignore unneeded answer blanks, and list points in lexicographic order. I...

Show that if we have N positive numbers \left[ p_{i}\right]_{i=1}^{N} such that \sum_{i} p_{i} =1 then for any N numbers \left\{x_{i}\right\}_{i=1}^{N} we have the inequality \prod_{i=1}^{N} x_{i}^{2 p_{i}} \leq \sum_{i=1}^{N} p_{i}x_{i}^{2} So I am thinking...

A long first post, but not too hard! dont worry about this i already solved it thanks anyway! The lagrangian of a particle of mass m moving under constant gravity is \mathcal{L} = \frac{1}{2} m (\dot{x}^2 + \dot{z}^2 - mgz = \frac{1}{2}m (\dot{\rho}^2 + \rho^2 \dot{\phi}^2) - mg \rho...

I need to find the extrema of f(x,y,z)=x+y+z subject to the restraints of x^2 - y^2 = 1 and 2x+z = 1. So the gradient of f equals (1,1,1) = lambda1(2x,-2y,0) + lambda2(2,0,1). Solving for the lambdas I found that lambda1 = -1/(2x) = -1/(2y), or x=y. But this isn't possible if x^2 - y^2 = 1...

I'm stuck on the following question "Find the maximum and minimum values of f(x,y,z) = x^2y^2-y^2z^2 + z^2x^2 subject to the constraint of x^2 + y^2 + z^2 = 1 by using the method of lagrange multipliers. Write the 4 points where the minimum value is achieved and the 8 points where the...

Hi all, I was wondering how to go about solving an optimization problem for a function f(x,y,z) where the two constraint equations are given by: a is less than or equal to g(x,y,z) is less than or equal to b (a and b are two distinct numbers) h(x,y,z) is less than or equal to c (c is...

Help Please! Studying for test : Lagrange Multipliers! Good morning all. I am having trouble with the next step to the following problem: Q.Find all realtive extrema of x^2y^2 subject to the constraint 4x^2 + y^2 = 8. g(x)= x^2y^2 f(x) = 4x^2 + y^2 = 8. the gradiant of f = <8x,2y>...

Hi, I'm having trouble with the following question. Q. Find the maximum and minimum of the function f(x,y) = x^2 + xy + y^2 on the circle x^2 + y^2 = 1. I started off by writing: Let g(x,y) = x^2 + y^2 then \nabla f = \lambda \nabla g,g\left( {x,y} \right) = 1 \Rightarrow 2x + y...

LaGrange Multipliers! Help! Use the Lagrange multiplier method for 3 variables to find the points on the surface 3xy-z^2=1 that are closest to the origin. I tried using the gradient= lamda(granient) and ended up getting (-3/2,0,-1). but i think i did it way wrong. Can someone please help...

Find the shortest and longest distance from the origin to the curve x^2 + xy + y^2=16 and give a geometric interpretation...the hint given is to find the maximum of x^2+y^2 i am not sure what to do for this problem thanks

For the proof of lagrange multipliers, it is based on the assumption that the function you are optimizing, f(x,y,z), takes on an extreme value at the point (x0,y0,z0), and that any curve that passes through this point has the tangent vector perpendicular to the gradient vector. That seems fair...

I'm not entirely sure what the english terms are for some of the things I'm about to say but i hope it's clear what I mean exactly. I'n my handbook the theorom is said to be: Say G is a part (wich is open) of R^n, f and g are functions from G to R (f:G->R, g:G->R) and both are differentiable...

Greetings all, Find the max and min values of f(x,y.z)=3x-y-3z subject to x+y-z=0, x^(2)+2z^(2)=1 can anybody help me get this problem started. thanks

Use Lagrange Multipliers to prove that the triangle with the maximum area that has a given perimeter p is equilateral. [Hint: Use Heron’s formula for the area of a triangle: A = sqrt[s(s - x)(s - y)(s - z)] where s = p/2 and x, y, and z are the lengths of the sides.] I have no idea how to do...

It has been a while and trying to brush up on LaGrange points. I want to find the highest and lowest points on the ellipse of the intersection of the cone: x^2+y^2-z^2 ;subject to the single constraint: x+2y+3z=3 (plane). I want to find the points and I am not concerned with the minimum and...

A bit of a tough one! Find the maximum of ln x + ln y + 3 ln z on part of the sphere x^2 + y^2 + z^2 = 5r^2 where x>0, y>0 and z>0. I know I need to use Lagrange multipliers but how should I go about it? Any help would be appreciated thanks!

Hi, I'm really stuck on this problem and I need some help?? Here's the question: The intersection of the elliptic paraboloid z=x^2+4y^2 and the right circular cylinder x^2+y^2=1. Use Lagrange multipliers to find the highest and lowest points on the curve of intersection. Your help will...

Find max and min value…f(x,y,z) =3x+2y+z; x2 + y2+z2 = 1 If g(x,y,z) = x2 + y2+z2 = 1 then what do I do next? I need help to further solve for this please? I am horrible at math and don't understand lagrange multipiers so can anyone better explain it to me and help me solve for difficult...