Optimization Definition and 588 Threads

Hello there! I was decorating my Christmas tree recently, and for some strange reason, I thought: "Hrm, I wonder if I could come up with an optimization problem where I have a definite length of lights/garland, and want to have equal space between each strand of lights/garland as they go around...

Homework Statement You are a lab technician and must create 250 ml of a 17% solution. You have availible three stock solutions. You have a one liter container of a 5% salt, a 500 l contained of a 28% salt solution, and a 400 ml container of a 40% salt solution. Show the work necessary to...

Just curious if Newton's method in high dimensions should always quickly converge to a min/max or saddle point. I can't seem to get the value of my gradient below 12-16; so, its not "diverging" but its not converging either. I want to avoid saddle points so I'm using Fletcher-Reeves method...

The manager of a department store wants to build a 600 square foot rectangular enclosure on the store's parking lot in order to display some equipment. Three sides of the enclosure will be built of redwood fencing at a cost of $7 per running foot. The fourth side will be built of cement blocks...

Hi, I work in NRM and need for some reason to optimize an objective function of the form ||M-M_target||^2 where M is the product of a large number (>100) 2D unitary complex matrices (Qi) and a vector (A), i.e. M=Q1*Q2*...*QN*A, and M_target is a constant complex vector. I can do it directly...

A cylindrical can with height h and radius r is to be used to store vegetarian chilli. It is to be made with 6 square centimetres of tin. Find the height h and radius r which maximizes the volume of the can. Hint: The volume of a cylinder is r2h and the surface area of the side walls of a...

So I have a problem. The problem says: A fence 8 ft tall rubs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? I drew a picture to help, but I can't draw it...

Homework Statement Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 3. Homework Equations V=π*r^2*h/3 A=πr^2 + πrl The Attempt at a Solution I did multiple things that I'm not sure are correct. I took the derivative for the volume with the value of...

Homework Statement what is the maximum volume of an open top box that can be created with 300m sq of metal assuming none is wasted? Homework Equations The Attempt at a Solution so that means the surface area of the box must total 300 m sq so A(l,w,h)= lw + 2lh + 2wh = 300...

I have an optimization problem which am not able to figure out after much thought. Any suggestions on how to go about it are welcome. Thanks in advance. given a set of 'n' numbers. I have to find the optimal disjoint subset distribution of the set which minimizes the value given by a function...

Homework Statement I need to optimise a couple of equations. I want maximum S for minimum x. Constants: h, t Variables: w, jHomework Equations S = ( (j) / (j + 0.5*w) )^2 [Eqn 1] x = (const) * (j / w) [Eqn 2] [See attachment] The Attempt at a Solution Well... I've tried to re-arrange...

IS there a standard in the field for books on optimization theory. I'd like to possibly do a self-study on the subject. Thanks for the info!

Hi all, I have this kind of optimization problem: Variable to control: A=A=[a1;a2;...;am] objective function to minimize: L=A*TL where L is a scalar T is a matrix [1,m] TL is a matrix [m,1] constrain: Dt>Dtv where: Dt=[dt1;dt2;...;dtn] Dtv=[dtv1;dtv2;...;dtvn] is a...

Homework Statement A real estate company owns 180 apartments, which are fully occupied when the rent is $300. The company estimates that for each $10 increase in rent, 5 apartments will become unoccupied. What rent should be charged so that the company will receive the max income? Homework...

Hi all, Hopefully this is the right section for my post, if not I apologize. I'm hoping I can just get some advice to help me get started in the right direction. I am trying to do a mathematical inversion for the following: \frac{1}{N(zi)} \frac{dN}{dz}|_{z=zi} = -\frac{2}{zi} -...

1) How to justify if there is a tie for the minimum b-ratio at some iteration of the phase II simplex algorithm, then the next basic feasible solution is degenerate. I have no idea how to justify it. Please give me some direction 2) Max. z = transpose of C * the vector x s.t...

Homework Statement The fuel consumption of a river boat is kv3 litres per hour where k is a constant and v km/h is it's speed through the water throughout this question v > 4 km/h. i) determine the fuel consumption for a trip of x km against a current of 4km/h and find the speed at which...

For my economics/game theory thesis I need to optimize a function subject to an inequality constraint. maximize f(x1, x2) = 1/(x1+x2+y1+y2-w) subject to g(x1, x2) = x1+x2+y1+y2 < w This isn't particularly important, but the x and y variables are quantity of production by a firm. The objective...

Question: Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated a particles. For what value of q/Q>0.5 will the electrostatic force between the two parts have 1/5 of the maximum possible value? Attempt: F = [...

Homework Statement A coffee firm sells "Premium blend" and "Economy blend" coffee. Both are blended from three basic grades of coffee, A, B and C: Premium blend = 50% A + 40% B + 10% C Economy blend = 10% A + 40% B + 50% C The market prices are $1130/tonne for Premium and $750/tonne for...

Homework Statement I am doing an assignment in my Linear Algebra class. But I don't know how I will go about solving this problem. So the problem is a network of water pipes. I start with a matrix and I get the solution to the system from the RREF matrix. All the flow directions are set, so...

Well, I'm having trouble doing optimization problems (maximizing and/or minimizing a function in more then one variable with/without constraints). Would be a great help if someone could give me some good links on this topic or some methods generally. If the domain is compact; where are the...

I have some understanding of how to solve problems involving compact domains. Set the gradient to zero and solve for x and y, and then try to parameterize if needed to find max/min over the border of the domain. The thing is, my book doesn't go into much detail on how to do optimize functions...

Hello, I am working on a research project that requires me to write a solver for solving a particular problem. I could really use some math advice if anyone is willing to assist. I need to minimize a non-linear objective functions of 5 variables. It is a pretty complex function. Each of the...

Homework Statement A 5324 cubic foot tank with square base and an open top is to be constructed of a sheet of steel of a given thickness. Find the length of a side of the square base of the tank with minimum weight.Homework Equations The Attempt at a Solution I'm usually fairly decent at...

My friend and I have come across this problem in Apostol's Calculus Vol. 1, ed.2 (exercises 4.21 if anyone is looking). We are studying calculus independently and have become stumped by this one. Homework Statement The problem as written in Apostol: "A farmer wishes to enclose a rectangular...

Homework Statement A farmer wishes to enclose a pen in the shape of a right triangle with 100 ft of fencing. Set up the equation to find the maximum and minimum dimensions but do not solve the problem. Homework Equations I know the area for a triangle is simply A=1/2B*H and that the...

Homework Statement A construction company has been offered a contract for $7.8 million to construct and operate a trucking route for five years to transport ore from a mine site to a smelter. The smelter is located on a major highway, and the mine is 3 km into a heavily forested area off...

hi, I'm kind of new to optimization theory, and I have to maximize a multi-dimensional problem where I know the exact gradient and hessian. In other words, techniques such as BFGS are not sufficient because I don't want to approximate the Hessian (with an initial guess for example of H=I), I...

Homework Statement I took a test today on integration, curve sketching, and optimization. I am pretty sure that I got a 100 on it due to all the help here on PF with indef. integration and all of the helpful u-sub advice I have received. Anyway, there was 5 optimization word problems, and...

Homework Statement Stewart Calculus 6E: 4.7 #14 A rectangular storage container with an open top is to have a volume of 10m³. The length of it's base is twice the width. Material for the base costs $10 per square meter. Material for the sides cost $6 per square meter. Find the cost of...

Homework Statement #56.) Someone makes necklaces and sells them for 10 dollars each. His average sales were 20 per day. When he raises the price to 11 dollars per day, the average sales drops 2. a.)Find the demand function, assuming it is linear. b.)If the material to make each necklace...

Homework Statement a metal box with square base a no top holds 1000 cubic centimeters. it is formed by folding up the sides of the flattened pattern picture and seaming up the four sides. the material for the box costs $1.00 per square meter and the cost to seam the sides is 5 cents per meter...

1. Find the dimensions of the rectangle with the largest area that can be inscribed in the upper semi-circle given by x^2+y^2 ≤ 16, y≥0. 2. I thought I'd use A=lw 3. This is but a guess..so take it with a grain of salt.. height=2x base= x^2+y^2 A(x) = 2x(x^2+y^2) = 2x^3+2xy^2 A'(x) =...

I am having trouble conceptualizing a calculus optimization problem. I can find the answer to the problem by using the procedure but i am quite uncertain of how the equations match up with what's actually going on in the situation! Problem: What is the max length of widthless rigid pole that...

Homework Statement From all positive numbers x and y that hold y(x+2) = 9 , find the two numbers whose sum x+y is minimal The Attempt at a Solution Attached. My idea here is to take the derivative of y with respect to x, and set it equal to zero. This is how I understand you solve...

Homework Statement [PLAIN]http://img593.imageshack.us/img593/7536/unledci.png Homework Equations The Attempt at a Solution I called the wall b, half the roof a, and the angle theta. I get Area=2ab*sin(theta/2)+1/2 a^2 sin(theta)... try differentiating with respect to a and...

I'm going through a calculus textbook in an attempt to learn it myself. So far so good, but I've been stuck on optimization problems. I understand the concept. The maxima and minima of a function can be found by looking at where its derivative = 0. I also see that a function that has no...

Hi, I want to know the solution of the following equation. a = argmin_{a}[\sum{||a^Tx_i - y_i||^2}+\alpha ||a||^2] \\ where x_i, y_i are column vectors of dimensions m and n respectively where m>n. \alpha is a scalar and Y = a^T X where X=[x_1 x_2 ... x_k], Y = [y_1 y_2 ... y_k] I...

Would the optimal trading strategy for this stockmarket optimization fantasy be trivial or nearly impossible to compute? -or something in between? You have an initial amount of money A_o and your goal is to maximize the amount of money you will have at the end of a year by trading stocks...

Design the optimal conical container that has a cover and has walls of negligible thickness. The container is to hold 0.5 m^3. Design it so that the areas of its base and sides are minimized. information : 1) areas of the sides = (pi) x r x s 2) areas of the base = (pi) x (r^2) 3)volume of...

Homework Statement A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.30/square foot, the material for the sides costs $0.10/square foot, and the material for the top costs $0.20/square foot, determine the dimensions of the box that can be...

Hi, If we have a problem with two n-dimensional vectors, can we still apply Newton method to find the minimum point? Regards

I need to optimize a maximum likelihood function with many many variables (~10^2 variables). what is the faster method? thanx

Homework Statement A load must be suspended 6m below a high ceiling using cables attached to two supports that are 2m apart. How fare below the ceiling (x in figure) should the cables be joined to minimize the total length of the cable used? They give a figure, which I am butchering here...

Hi, I have a problem to solve using a sequential optimization algorithm. But since there are many algorithms, I am now confused which one to use. Which one is the most efficient? Thanks

Homework Statement Optimization (Maximize or Minimize) JJCJ=-x +2y according to: A(1,2) B(-1,2) C(-1,-3) Homework Equations The Attempt at a Solution I have taken many advanced math courses and its kind of embarrassing that I don't know how to approach this question :\...

Homework Statement Find the positive number that exceeds its square by the largest amount. Obviously this is on the open interval (0,1). Homework Equations The Attempt at a Solution F(x) = ( \frac{1}{n} ) ^2 - n \Rightarrow F'(x) = \frac{-2}{n^3} - 1 = 0 \Rightarrow 1 =...

Homework Statement The length of a cedar chest is twice its width. The cost/dm^2 of the lid is four times the cost/dm^2 of the rest of the cedar chest. If the volume of the cedar chest is 1440 dm^3, find the dimensions so that the cost is a minimum. Homework Equations LWH = 1440 W = 2L...

Hi all, I am working on a project and stuck at the following problem. Find vector x_{n\times 1} which minimizes the function f(x) = \sum_{i}^{n}x_{i}^{2} subject to the linear equality constraint [A]_{m\times n} x_{n \times 1}=b_{m\times 1} with m\leq n The function f(x) trivially...