Optimization — 400 discussions

How do I set up an optimization problem?? Homework Statement A closed reactangular box, with a square base x by x cm and height h cm. The surface area is 8cm^2. Find the maximum * I know how to find the critical points and everything else, but I don't know how set the problem up. I have a...

Hi all, I'm not quite sure if this is the right place to post my question, so forgive me if its not... I've written a program in Python that analyses data that I got from a compression experiment (mechanical testing of rocks and such), and I've written a piece of code that estimates the...

Homework Statement In general, I've been given a few functions of two variables, x and y. I have been asked to find all critical points by setting the gradient of the function equal to 0. Further we are asked to classify these critical points using some given rules regarding the Hessian...

I am looking for a term to describe a sort of "optimization" that I am trying to do. Hi everybody, I am a college student who unfortunately is not smart enough to be a math major. But nonetheless I am obsessed with statistics and numbers. I have a question: I need help figuring out a term...

Hello guys I have to maximise x1+1.2*x2+1.5*x3 subject 2*x3<=60 2*x2<=45 2*x1+x2+3*x3<=80 x1>=20 x2+x3>=10 x1,x2,x3>=0 I am told that one of the constraints is redundant i.e one of the equations can be removed and then use the Simplex method to obtain the values for x1,x2,x3. The problem is...

PROBLEM STATEMENT: Determine if f(x,y) = x^2+y^2 has a maximum and a minimum when we have the constraint 2x^3+3x^{2}y+3xy^{2}+2y^3=1. (1) ATTEMPT TO SOLUTION: A standard way of solving these kinds of problems is by using the Lagrangian multiplier-method. It consists of comparing the gradient of...

Hello, I need some assistance with Mathematica. I'm very new to the software, and am not very familiar with the programming language. I guess I'm a little bit lost as to where to go after defining my function. I'm not sure how to apply constraints, or really how to jump in and tackle this...

Homework Statement A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacks 20 miles apart, the concentration of the combined deposits on the line joining them, at a distance x from one stack, is...

We were given a small project to do before a test in my engineering statics class, i understand the goals of the project and understand the steps i need to take (i believe) however i don't understand how to simplify the distributed load into something i can anylize as we haven't seen anything...

Homework Statement Find the global max/min for z=xy^2 - 5 on the region bounded by y=x and y=1-x^2 in the xy-plane. Homework Equations The Attempt at a Solution I found the critical point of z=xy^2 - 5 at (0,0), but I do not know how to relate this to the boundary.

Well, I've been working on this problem, but I can't get the right path to the solution. Homework Statement "Consider the following version of the Ehrlich economic model of crime where an individual has the expected utility function: U = p ln(Iu) + (1 - p) ln (Is). p = objective...

I am trying to figure out how the least squares formula is derived. With the error function as Ei = yi - Ʃj xij aj the sum of the errors is SSE = Ʃi Ei2 so the 1st partial derivative of SSE with respect to aj is ∂SSE / ∂aj = Ʃi 2 Ei ( ∂Ei / ∂aj ) with the 1st partial derivative of...

Sometimes I wonder why the optimization conditions you can find mathematically, show how a system behaves in nature. As an example you can calculate mathematically what curve a hanging rope will form such that its potential energy is minimized. But how do you know that there does not exist...

Hello guys, I work on a final project study discussed the use of optimization methods. The project in question consists in partitioning a grid dimensions NXM grids in dimensions 3 X 3 (which share no box) to the extent possible, otherwise find grids of dimensions 3 x 3 which are dependent...

Currently I am doing models for my system. I have finished all of them designing three defferent controllers (Feedback Linearization Controller FLC , Sliding Mode Controller SMC and Fuzzy Sliding Mode Controller FSMC).Now I am asked to optimize the FSMC using Gentic Algorithms but I have no idea...

Homework Statement a cylinder can be inscribed upright in a circular cone with radius 4 and height 7. What is the maximum volume of a cylinder that can be inscribed inside of the cone.Homework Equations Image of the problem http://s17.postimage.org/67akeibxb/Cylinder.png The Attempt at a...

I have an optimization problem and I am looking for a method rather than a solution here. I'll state it in a general form. Let there be two functions: f_1(x_1,\cdots, x_n,y_1,\cdots, y_n ) and f_2(x_1,\cdots x_n,y_1,\cdots, y_n ). Maximize f_1 with regards to variables x_1,\cdots, x_n with...

Homework Statement If the area of the window is 3m² what are the dimensions of a rectangle and (isosceles)triangle that will minimize the perimeter. http://s12.postimage.org/r1czis8jh/optimize.png --DIAGRAM Homework Equations Let AreaTotal=3 Let Areatotal=Atriangle+Arectangle Arectangle=lxw...

Hi everyone, I have some trouble adapting an existing fortran code for my application. In the following Module I am optimizing a value for two planes ( i = iplan one&two). In order to do that, I need to assign ten certain values from an external inp. file for each plane. I have two loops...

Hello, My question is as follows. Is it possible to obtain a closed form solution to \displaystyle \max_{\xi\ge 0, \lambda\ge 0}\,\, -\frac{1}{2}\||\xi\||^2 +(\xi,\,\lambda) -\frac{1}{2}\||\lambda\||^2 Here \xi and \lambda are vectors. Thank you.

Homework Statement Albany is 12km north of Rochedale. Bells Creek is 5km west of Albany. The road is to be repaired and repairs cost $96 000 per km. The cost of laying a new road is $120 000 per km. It has been decided to repair the old road from Rochedale as far as point K, and then to...

Homework Statement A manufacturer wants to design a box having a square base and a surface area of 108m^2. What dimension will produce a box with maximum volume?Homework Equations a=x^2+4xy V=x^2y a=108m^2 The Attempt at a Solution

Hi! Probably quite easy for you guys (Im not even sure I am in the right thread). The assignment is in constrained optimization, and we're supposed to use lagrange to find the point on the parabola y=x^2 which is closes to (2, 1). I've been trying for a while and can't seem to find the right...

Homework Statement Please see attached thumbnail Here's what I know. 1)Bk is the Hessian 2) sk = \alpha*p 3)pk is the search direction 4) Alpha is the step size Homework Equations yk = \nablaf(xk+1) -\nablaf(xk Bk+1(xk+1-xk) = \nablaf(xk+1) -\nablaf(xk The Attempt at a Solution...

Homework Statement A life guard sitting on a beach at point A needs to get to point B (Hasselhoff fell out his inflatable rocking chair) as soon as possible. The lifeguard (Pamela Anderson) can run (on the shore in slow-motion, like in Baywatch) at a rate of 3 m/s and can swim at a rate of 1.5...

Homework Statement the base of an aquarium with given volume V is made of slate and the sides are made of glass. if slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. Homework Equations The Attempt...

Homework Statement Through market research, a computer manufacturer found that x thousand units of its new laptop will sell at a price of 2000 - 5x dollars per unit. The cost, C, in dollars of producing this many units is C(x) = 15 000 000 +1 800 000x + 75x^2. Determine the level of sales that...

Homework Statement Two isolated farms are 12km apart on a straight country road that runs parallel to the main highway 20km away. The power company decides to run a wire from the highway to the junction box, and from there, wired of equal length to two houses. Where should the junction box...

Homework Statement An isosceles triangle has a rectangle inside of it with length 2 cm and width 6 cm. What angle ∅ will give the triangle the minimum area. Homework Equations A =1/2 (bh) The Attempt at a Solution

Hey guys, 1. basically I am using the silvaco athena and i got some code to make the solar cell simulation. and my project is basically about designing pn junction in terms of the solar cell. kinda clueless of what are things that i need to modify in the code to make sure that i have a good...

Homework Statement A(\vec{x}) = (F + T * x )2 F is a constant, x is a 2×1 vector T is a (constant) 1×2 matrixB(\vec{x}) = || K.Z.x ||2 k:3\times3 matrix and Z:3\times2, x the same as aboveB(x) is also R2→RC(x) = A(x) + B(x) Homework Equations 1- I am confused...

A farmer wishes to build a rectangular chicken coop with as close to, but not greater than N square units. He wants to purchase the least amount of fencing possible, but fencing can only be purchase by the integer foot. How does he do this? P = 2x+2y N = xy y=N/x P = 2x + 2(N/x) P' =...

Hello everyone, This is my first post on here, I was hoping it wouldn't be asking for help but I don't have any options left and it's a problem that is due soon. I promise I have tried to solve it myself but I'm unsure if I'm doing it correctly and it is part of a take home test. Homework...

Homework Statement I have a whole two courseworks on Genetic Algorithms, but we have been shown no examples. I am stumped! 1. A function f is set to depend on five variables x1, . . . , x5 where x1 can take 2 different values, x2 can take 8 different values and x3, x4, x5 each take 4 different...

Homework Statement The printed area of a page in a book will be 81cm^2. The margins at the top and bottom of the page will each be 3cm deep. The margins at the sides of the page will each be 2cm wide. What page dimensions will minimize the amount of paper? Homework Equations Area=...

Hello everyone! I'm trying to solve a linear optimization problem with a large-dimension matrix, MATLAB says memory is full. What to do? Thanks!

Homework Statement Build a steel drum (right circular cylinder) of fixed volume V. The cost of the material is the same for the top and sides (same gage and same cost) and disregard waste. What is the relationship between the height of the radius that will minimize the surface area of the...

Calculus Homework Help -- Optimization Word Problem I'm in a University Calculus class, and I am having trouble with one of my homework questions. Much help would be appreciated! "Determine the height and radius of the cylinder of greatest volume that can be inscribed in a sphere of radius...

Homework Statement The electrostatic potential at each point in the region 4x^2 + 9y^2 <= 36 is given by f(x,y) = 3x^2 + 2xy - y^2 + 5. Find the maximum potentials in the region. (Without using Lagrange Multipliers). The solution also said how to do it with Lagrange Multipliers but I...

Homework Statement I have a sector of a circle with area 12 square meters. If radius r and angle \theta are chosen so that the that perimeter of the sector is the smallest possible, then what is the radius? Homework Equations I have area of sector as A=\frac{\theta r^2}{2} which is 12...

Just reviewing for a chapter test... I've always found optimization problems easy, but I don't have answers for these review questions so I thought I'd check my work on here. Homework Statement A piece of cardboard is 14 inches by 10 inches and you are going to cut out the corners and fold up...

Homework Statement Homework Equations Constrined optimzation The Attempt at a Solution ("o" means dot product) Let M={x|Ax=c} and f(x)=(1/2)x o Qx - b o x Suppose x0 is a local min point. Suppose, on the contrary, that x0 is NOT a global min point. Then there must exist a...

Dear forum, I am new here, so hi to all! I am using Madgraph to generate some events about exotic physics. The problem is that when I give this line gg>(rho>(pip>j j)(pip>j j))(rho>(pip>j j)(pip>j j)) All these are declared in the particles.dat file. The problem is that it takes too much...

Homework Statement Hello! I'm having some difficulty getting the objective function out of this question, any help/hints would be appreciated >.< Company A prepares to launch a new brand of tablet computers. Their strategy is to release the first batch with the initial price of p_1 dollars...

Hi There, What's the best core loading pattern optimization method? I believe this is very depended to experts knowledge, I mean the methods such as Genetic Algorithm or Neural Network or Ant Colony are not so useful for such these optimization. Please correct me if I'm wrong on this. Thanks

Hi, I have formulated what I believe to be a generalized(to some degree) optimization under uncertainty problem. The write up is included in the attached file. I would appreciate any and all input, help or guidance as to how this problem could be solved. If you have any questions please feel...

Hi guys, me and my fellow classmate have been working on a math problem we believe to be a Modeling and Optimization type problem in our calculus class. We've been at it for 2 days now! Just can't seem to figure it out... We'd really like appreciate and all help! Homework Statement [There is...

hi all, I would like to be regarded as a novice on the subject matter. I am doing a research on optimization of animal fence wire. the idea basically is that, i want to improve on the existing design of wire used for animal fencing to minimize the chances of animals breaking out of fence...

Homework Statement A wire 6 meters long is cut into twelve pieces, eight of one length and four of another. These pieces are welded together at right angles to form the frame of a box with a square base. a) Where should the cuts be made to maximize the volume of the box? b) Where should the...

Hi I am having a lot of trouble with this problem. I don't actually know where to begin. A box with a square base and open top must have a volume of 62,500 cm3. Find the dimensions of the box that minimize the amount of material used. Need to find: sides of base cm height...