Optimization — 400 discussions

i need a decent book for linear and non linear optimization. Currently i am using Linear and Non linear optimization by Griva Nash and Sofer, and it is by far the worst math book i have ever used. It does not have any solved examples or anything. It does not even have any proofs. It has...

Homework Statement minimiza f(x) = x_1 subject to (x-1)^2+y^2=1 (x+1)^2+y^2=1 Graph the feasible set, Are there any local minimizers and global minimizers? Homework Equations I have graphed the feasible set...

Homework Statement A piece of wire 12 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (Give your answers correct to two decimal places.) Part A) how much of the wire should be used for the circle to maximize the area? (Solved this part...

Homework Statement The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm2, find the dimensions of the poster with the smallest area. Homework Equations Area of a rectangle is length...

Homework Statement Consider a feasible region S defined by a set of linear constraints S = {x:Ax<b} Prove that S is convex Homework Equations All what i know is that, a set is convex if and only if the elements x, and y of S ax + (1-a)y belongs to S for all 0 <a < 1 The...

Say, I want to design, 220 / 12 V 100VA transformer. We have V = 4.4BfNA (V is applied voltage RMS, B is peak flux Density, N is no. of turns, f is frequency, A is core cross section) so, B = V / (4.4 f NA) If i use iron core, there is limit to the maximum value of B without excessive...

Homework Statement Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row her boat at 5 mph and can walk at 3 mph. Where should she land her boat to reach the village in the least amount of time...

Homework Statement A triangle has adjacent sides 4 cm and 6 cm. Find the angle contained by the sides which maximizes the area. Homework Equations The Attempt at a Solution I'm not going to lie. I have no idea how to start this. I tried using sine law to create a helper equation...

the value same which maximizes the logarithm of the function and the plain form of the function why?? please help me, thanks

Optimization under differentiation! Homework Statement OK I have a upside down looking curve structure (½ ellipse). It has the following specifications: The building has a rectangular base 150m long and 72m wide. The max height of the structure should not exceed 75% of its width or be less...

1) The question A rectangular pen is to be built with 1200 m of fencing. The pen is to be divided into three parts using two parallel partitions. A) Find the maximum possible area of the pen. (45000 m^2) B) explain how the maximum area would change if each side of the pen had to be at least...

Homework Statement From a square piece of cardboard, 30 cm on each side, an open topped box is to be constructed by cutting the squares from the corners and turning up the sides. What are the dimensions of the box of largest volume? The Attempt at a Solution I know how to do...

Homework Statement a line passes through the point (1,1/8) and intersects the positive x-axis at the point A and the positive y-axis at the point B. What is the shortest possible distance between A and B? Homework Equations i came up with three slopes for this line m1=-b/a...

Homework Statement A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. If building the tank covers $10 per square meter for the base and $5 per square meter for the sides, what...

Homework Statement Find the critical points of the function. Then use the second derivative test to determine whether they are local minima or maxima(or state that the test fails). f(x,y)=(x-y)(e(x2-y2)) The Attempt at a Solution fx=(x-y)(2x(e(x2-y2)))+(e(x2-y2))=0...

Homework Statement A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder. Homework Equations Vcone = (1/3)(pi)(r2)(h) Vcylinder = (pi)(r2)(h) The Attempt at a Solution I've been trying to relate the...

Homework Statement A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. If it is to be partially submerged in the liquids as to maximize the exposed wetted area of the disk, show that the center of the disk should be positioned at a height r/ \sqrt{1+\pi^2}...

Homework Statement Hello, If you don’t mind, would you all be able to look over these problems for me? I have left out much of the ‘algebra’ work for the sake of space…so please let me know if you think there are any algebra errors. In addition I am particularly looking to see if I have set...

Homework Statement UPS will only accept packages with a length of no more than 108 inches and length plus girth of no more than 165 inches. Assumign that the front face of the package is square, what is the largest volume package that UPS will accept? Assuming the package looks like this...

Homework Statement - Building a half cylinder structure. - The structure must have an exact volume of 225,000 cubic feet. - The current construction costs for the foundation are $30 per square foot, the sides cost $20 per square foot, and the roofing costs $15 per square foot. - Minimize the...

We have just begun this topic and I'm really confused about how to approach questions, is there any trick or guideline for doing so? Ex: Consider an isosceles right triangle whose hypotenuse is the x-axis and whose vertex is on the y-axis. If the hypotenuse is 2 units long, we'd have...

Homework Statement Problem 2 b) in the following link http://www.math.ubc.ca/~haber/courses/math253/Welcome_files/asgn4.pdf" Homework Equations V=pi(r1r2)H SA=? The Attempt at a Solution I was thinking I should form two equations V=10=pi(r1r2)h and then an equation for the...

Homework Statement The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $600 per person per day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then each fare is reduced by $4...

See if anyone can help me with this: Among all triangles of perimeter equal to P, find the one with the largest area. (Hint: use the formula A=\sqrt[ ]{p(p-x)(p-y)(p-z)} where P=2p, P is the perimeter). So, I have f|_s , I think that must be solved using Lagrange multipliers, at least I don't...

Homework Statement http://i53.tinypic.com/1zu5ty.jpg The Attempt at a Solution well so far, all i got is 3x + y = 3000; also y = 1000/x ==>> 3x+ (1000/x) = 3000 i don't know what the area should be though... would it be A=x2y If i am right in that, would i do this after i...

Dear all, I have a least square optimization problem stated as below \xi(z_1, z_2) = \sum_{i=1}^{M} ||r(z_1, z_2)||^2 where \xi denotes the cost function and r denotes the residual and is a complex function of z_1, z_2. My question is around ||\cdot||. Many textbooks only deal with...

Homework Statement A right angle is moved along the diameter of a circle of radius a (see diagram). What is the greatest possible length (A+B) intercepted on it by the circle. Homework Equations so, the pythagorean theorem might be useful diameter = 2a The Attempt at a Solution...

Homework Statement Find the abs max and abs min values of the function f(x) = -2x^2 + 3x + 6x^(2/3) + 2. Homework Equations The Attempt at a Solution So the candidates are the endpoints, where f'(x) = 0, and where f(x) DNE. f(-1) = 3 f(3) = 5.481 For the derivative of...

1. Hey all, For my calculus class we were giving the problem of solving for the optimization of a tin can using differential calculus. The problem was to find the minimum cost for any tin can of any height(as well as using the equation for the tin we had). The surface area of the cylinder was...

Hi, I'm trying to do a constrained optimization problem. I shall omit the details as I don't think they're important to my issue. Let f:\mathbb R^n \to \mathbb R and c:\mathbb R^n \to \mathbb R^+\cup\{0\} be differentiable functions, where \mathbb R^+ = \left\{ x \in \mathbb R : x> 0...

hi I have an idea for new logic optimization algorithm, like "Quine–McCluskey algorithm" and the "Espresso heuristic logic minimizer", but it can handle multi-level representations and it can find the (theoretical) best circuit. It should work for 8 to 12 input bits. I was wondering if such...

This isn't a homework question, although I am in a calculus course. I'm a little fuzzy on the method that I was taught (discover intervals and all that nonsense to make sure f'(x)=0 is a max or a min). I was curious if, when I discovered the values of x such f'(x)=0, I could then find f''(x)=0...

Hi all, I've been stuck on this question for hours and hours, I'm not sure what I'm doing wrong.. The question states, "a new cottage is built across the river and 300 m downstream from the nearest telephone relay station. The river is 120 m wide. to wire the cottage for phone service, wire...

Homework Statement A conical tent must contain 40\pi ft^{3}. Compute the height and radius of the tent with minimal total surface area. (Include the floor material.) Homework Equations 1. \frac{\pi r^{2} h}{3} = 40\pi 2. \pi r \sqrt{r^{2} + h^{2}} + \pi r^{2} = S 3. \frac {dr}{dh} =...

hi i want to find values of a,b,c such that.. Minimize (a+b+c) constrained to (x-a)^2 + (y-b)^2 + (z-c)^2 less than equal to R(z) (x-a)^2 + (y-b)^2 + (z-c)^2 greater than equal to r(z) can anyone help me solving this?? which method should b used for better computation??

Homework Statement Two related type of questions: 1) A rectangular prismic net enclosure for practising golf shots is open at one end. Find the dimensions that will minimize the amount of netting needed and give a volume of 144 m3. Netting is only required on the sides, top, and the far...

Homework Statement Part 1: A forest in the shape of a 50km x 50 km square has firebreaks in rectangular strips 50km by 0.01 km. The trees between two fire breaks are called a stand of trees. All firebreaks in this forest are parallel to each other and to one edge of the forest, with the first...

Goal: You want to train your Senior Manager. He needs skills: x1, x2, x3, x4, x5, x6, x7, x8, x9, x10. You are to choose from the following programs/courses that fulfills all the senior manager's skill needs at the cheapest cost. p1 has x1, x3, x4 at $500 p2 has x3, x5, x9, x10 at $1000...

Hello, I am new in computational chemistry. I was calculating by "DFT and HF theory" (using GAUSSIAN 03W) molecular parameters of "2D coordination polymer, [Cd(μ-pydc)(2-mim)]n (pydc = pyridine-2,3-dicarboxylate, 2-mim = 2-methylimidazole)" . I have Crystallographic data are belong to this...

Homework Statement I need to optimize this given code: /* A struct used to compute averaged pixel value */ typedef struct { int red; int green; int blue; int num; } pixel_sum; /* Compute min and max of two integers, respectively */ static int min(int a, int b) { return (a < b ...

Homework Statement A right circular cone of base radius r and height h has a total surface area S and volume V . Show that 9V2=r2(S2-2pir2S) . (i can do this part) . Hence or otherwise , show that for a fixed surface area S , the maximum volume of the cone occurs when its semi-vertical angle...

Homework Statement I need to optimize this given code that rotates an image 90 degrees so it runs at least three times faster: void naive_rotate(int dim, pixel *src, pixel *dst) { int i, j; for (i = 0; i < dim; i++) for (j = 0; j < dim; j++) dst[RIDX(dim-1-j, i, dim)] =...

The problem states: The trough in the figure is to be made to the dimensions shown. Only the angle theta can be varied. What value of theta will maximize the troughs volume? http://img81.imageshack.us/img81/5963/24ni3.jpg (There is an image of the problem) I know the height in terms...

Is anyone able to give me some pointers. I am trying to brush up on my calculus I for my next calc class and I can't grasp optimization. I hated it then and I hate it now. I can do everything else in calculus I except this and it's so irritating. I can learn every integration rule in Calc I in a...

1.http://www.teachingcenter.ufl.edu/materials/math_lab/oldtests/FA09_MAC2311_exam4ab.pdf Number 2 2. Maxamize XY subject to , y=sqrt(x) 3. I don't know what numbers to use...

Homework Statement Consider the half space defined by H = {x ∈ IRn | aT x +alpha ≥ 0} where a ∈ IRn and alpha ∈ IR are given. Formulate and solve the optimization problem for finding the point x in H that has the smallest Euclidean norm. Homework Equations The Attempt at a...

Homework Statement A rectangular storage container with an open top is to have a volume of 10 m^3. The length of this base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such...

Homework Statement Homework Equations Volume of cone= (1/3)*pi*r^2*h Volume of sphere= (4/3)*pi*r^3 Surface area of sphere 4*pi*r^2 The Attempt at a Solution primary equation is V(cone)= (1/3)pi*r^2*h---> V(cone)= (1/3)pi*(r-h/2)^2*h constraint: constraint:V(sphere)= (4/3)*pi*r^3 ***from...

Homework Statement The can will hold 280 mL of juice. The metal for the side of the can costs $0.75/m^2. The metal for the top and bottom costs $1.4/m^2. The side of the can is one rectangular sheet. The top and bottom are stamped out from another rectangular sheet, the unused metal from this...

Homework Statement Determine the maximum area of a rectangle formed in the region formed by the two curves y1=x2 - k y2=x2 + k Homework Equations The equations are given, I tried using k=1. so y1= x2 - 1, etc. The Attempt at a Solution Is it true that the rectangle has to be...