Optimization Definition and 588 Threads

1. Homework Statement [/b] f\left(x,y\right) = x^2 +y^2 g\left(x,y\right) = x^4+y^4 = 2 Find the maximum and minimum using Lagrange multiplier Homework Equations The Attempt at a Solution grad f = 2xi +2yj grad g= 4x^3i + 4y^3j grad f= λ grad g 2x=4x^3λ and 2y=...

Dear friends: anyone who used the materials studio software before? these days, i used the software to do the geometry optimization of a compound's structure. it has already taken about 30hours to do the optimization job till now and it has not finished yet. i am really anxious and don't know...

First let me clarify this is not a homework question. This part has cropped up as part of a small project i am doing on Cosmic microwave background. How would i go about minimizing the function f(x_{1},x_{2}...x_{n})=\Sigma*x_{i}*a_{i} subject to the constraint: \Sigma...

I am told in the problem that i am to minimize the amount of cardboard needed to make a rectangular box with no top have a volume of 256 in^3? I am to give dimensions of box and amount of cardboard needed. Can anyone help

Let P^ + ,P^ - ,I,Q \in R^{n\times n}, K\in R^{n\times 1}, M\in R^{1 \times n}, and assume that Q is positive definite, P^ - is positive semidefinite whence (MP^ - M^T + Q)^{ - 1} exists (where T denotes transpose). In what sense does K = P^ - M^T(MP^ - M^T + Q)^{ - 1} minimize the quadratic...

Homework Statement The volume of a cylindrical tin can with a top and a bottom is to be 16\pi cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can? Homework Equations V=\pir2h The Attempt at a Solution So I...

Protectionism is often viewed as positive for the country that implements the protectionism but bad globally due to losses of efficiency and miss allocation of resources. Because protections measures are often met with counter protectionist measures countries try to trade freely and fairly for...

Homework Statement The upper right-hand corner of a piece of paper, 12 in by 8 in is folded over to the bottom edge. How would you fold it to minimize the length of the fold? In other words, how would you choose x to minimize y? Homework Equations None so far. The Attempt at a...

A rectangle is to be inscribed in a right triangle having sides 6 inches, 8 inches, and 10 inches. Determine the dimensions of the rectangle with greatest area. I recently tried doing it and the answer was found by finding the slope and then using the first and second derivatives of the area...

My teacher was saying that it is possible to have no solution to an optimization problem, and I was curious about how this could be possible. Could someone please explain and possibly give an example?

Homework Statement Find the minimum distance from the origin to the curve y = e^x.Homework Equations Distance Formula The Attempt at a Solution http://carlodm.com/calc/prob6.jpg 5-6 bright Calculus kids in my high school grappled with this problem and we couldn't find an answer. Can...

F(x,y) = (2*y+1)*e^(x^2-y) Find critical point and prove there is only one. Use second derivative test to determine nature of crit. pt. I know the procedure in solving it: set partial derivatives to zero and solve resulting equations. And by second derivative test, if D>0, f(a,b) is local...

Homework Statement Question: You are planning to make an open rectangular box from a 10 by 18 cm piece of cardboard by cutting congruent squares from the corners and folding up the sides. 1) What are the dimensions of the box of largest volume you can make this way? 2) What is its...

1. The problem statement A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence? (Give the dimensions in increasing...

Homework Statement 1. A closed box of square base and volume 36 cm^3 is to be constructed and silver plated on the outside. Silver plating for the top and the base costs 40 cnets per cm^2 and silver plating for the sides costs 30 cents per cm^2. Calculat ethe cost of plating the box so that...

Homework Statement Consider the part of the parabola y=1-x^2 from x=-1 to x=1. This curve fits snugly inside an isosceles triangle with base on the x-axis and one vertex on the y-axis. What is the smallest possible area of such a triangle? The Attempt at a Solution A =...

My job is to maximize the area of the kite so that it will fly better, faster, higher. A kite frame is to be made from six pieces of wood. The four pieces that form its border have been cut the lengths. So one of the top border is 2 cm long and the bottom border is 4 cm. The total border length...

Hey all, I'm struggling to even start this problem: An evaporative cooler design uses a rotating wheel that is placed upright (vertical) and is partially submerged in water. The center of the circle is above the waterline. Let R be the radius of the wheel and x be the distance from the...

This is how the book describes the problem: If the ellipse x2/a2+y2/b2=1 is to enclose the circle x2+y2=2y, what values of a and b minimize the are of the ellipse? First of all I completed the square for the second equation and I got: x2+(y-1)2=1. I isolated the x2 and substituted it into...

Homework Statement "For this project we locate a trash dumpster in order to study its shape and constuction. We then attempt to determine the dimensions of a container of similar design that minimize construction cost." 1. (Already located, measured, and descibed a dumpster found). 2...

Hello everyone, My questions and link to my webpage is posted over at the original science forums. Please take a look: http://www.scienceforums.net/forum/showthread.php?t=36161 Cheers, Michael

Homework Statement look at jpg attachment Homework Equations T(y)=(z-y/r)+(sqrt(x^2+y^2)/s) ac=z bc=x dc=y ab=w im having trouble taking the derivative of T(y) and how to solve it on the second one i think there is no maximal area but there is a minimal but not sure how to...

Homework Statement A water tank is in the shape of an inverted conical cone with top radius of 20m and depth of 15m. Water is flowing into the tank at a rate of 0.1m^3/min. (a) How fast is the depth of water in the tank increasing when the depth is 5m? Water is now leaking from the...

Greetings, I'm working on a problem where I am to find the coordinates of the point (x,y,z) to the plane z=3x+2y+1, which is closest to the origin. I know that this is an optimization problem, and I believe I have to minimize (x,y,3x+2y+1). I started by finding partial derivative, fx, of the...

Hi, This is a question about a boolean "law" type behavior I've noticed in my homework a couple of times. Basically i can't find a boolean algebra law that permits this optimization short of using a k-map. So I'm just wondering if theirs some way to optimize the one equation using...

Homework Statement This isn't that hard but I cannot remember a nice Calculus way of doing it. I'm trying to find the ratio of height to diameter of a cylinder that produces the minimum material buckling (B_m)^2. The problem statement my professor provided states that the minimum is found at...

I met a problem about finding the optimization of some function. I used the Trust-Region Newton and Quasi-Newton methods for the problem; however, with different initial guesses I sometimes got the local minimums. May I ask how to get out the trap of the local minimums please? I may try the...

I met a problem about finding the optimization of some function. I used the Trust-Region Newton and Quasi-Newton methods for the problem; however, with different initial guesses I sometimes got the local minimums. May I ask how to get out the trap of the local minimums please? I may try the...

a chord AB of a circle subtends an angle that is not equal to 60 degees at a point C on the circumference. ABC has maximum area. then find A & B in terms of the angle.

Hi. I have a problem I am hoping you all can shed some light on. I have N entities, O, each described by N values - a weight W and N-1 similarity coefficients to the other N-1 entities. I guess we can represent Oi as (Wi, Sij, j=(1,2,...,N, i!=j)(?). Given an integer M and M < N I need to...

Homework Statement I need help on an optimization problem involving a hexagonal prism with no bottom or top, but the top is covered by a trihedral pyramid which has a displacement, x, such that the surface area of the object is at a minimum for a given volume. The assigned variables include...

I'm trying to find the regular parallelepiped with sides parallel to the coordinate axis inscribed in the ellipsoid x[2]/a[2] + y[2]/b[2] + z[2]/c[2] = 1 that has the largest volume. I've been trying the Lagrangian method: minimize f = (x)(y)(z), subject to the constraint (x[2]/a[2] + y[2]/b[2]...

Dear all, I am looking for some advise on optimization routines. I have a collection of 2D data (x-y plot) and a piece of code which generates different models based upon several inputs (a,b,c,d,etc). These inputs generate several outputs which characterize the final generated model...

I have a case where I am trying to find the optimal place to put 3 rivet points (I will maybe even test with 4). The rivet points r subject to a force according to the picture, which vary 360. What I am seeking here is mathematical methods to find the optimal place to put the 3 riverts, so that...

Homework Statement A train leaves the station at 10:00 and travels due south at a speed of 60 km/h. Another train has been heading due west at 45 km/h and reaches the same station at 11:00. At what time were the two trains closest together? Homework Equations c^{2}=a^{2}+b^{2}The Attempt at a...

[SOLVED] Optimization: Rectangle Inscribed in Triangle Homework Statement Please see http://www.jstor.org/pss/2686484 link. The problem I have is pretty much exactly the same as that dealt with in this excerpt. (focus on the bit with the heading "What is the biggest rectangle you can...

[SOLVED] Optimization problem Homework Statement A baseball team plays in the stadium that holds 60000 spectators. With the ticket price at 8 the average attendence has been 24000. When the price dropped to 7, the average attendence rose to 30,000. a) find the demand function p(x), where x...

Homework Statement An eight-foot fence stands on level ground is one foot from a telephone pole. Find the shortest ladder that will reach over the fence to the pole. Homework Equations Pythagoras? Derivative. The Attempt at a Solution The problem is I don't know how to start this...

1) http://www.geocities.com/asdfasdf23135/advcal28.JPG From the assumptions, I think that the mean value theorem and/or the extreme value theorem may be helpful in this problem, but I can't figure out how to apply them to reach the conclusion. Could someone please give me some general hints...

Hello! Here's a question that I couldn't understand; A canvas tent is to be constructed in the shape of a right-circular cone with the ground as base; Using the volume V and curved surface area S of the cone, V = \frac{1}{3}\pi r^2 h, S = \pi rl, Find the dimensions of the cone...

1a) Determine the maximum value of f(x,y,z)=(xyz)1/3 given that x,y,z are nonnegative numbers and x+y+z=k, k a constant. 1b) Use the result in (a) to show that if x,y,z are nonnegative numbers, then (xyz)1/3 < (x+y+z)/3 Attempt: 1a) Using the Lagrange Multiplier method, I get that the...

[SOLVED] one last optimization problems Homework Statement find two positive numbers such that the sum of the number and its reciprocal is as small as possible. Homework Equations x+(1/x) = s f' =1 + ln x The Attempt at a Solution lost

Homework Statement find the dimensions of a rectangle with perimeter 100m whose area is as large as possible Homework Equations area = XY 100 = 2x + 2y y= 100/4x x(100/4x) (400x - 400x)/16x^2 1/16x^2 = 0 The Attempt at a Solution well... am lost

[SOLVED] simple optimization problem Homework Statement find the dimensions of a rectangle with area 1000 m^2 whose perimeter is as small as possible Homework Equations perimeter = 2x + 2y area = xy 1000 = xy y= 1000/x perimeter = 2x + 2(1000/x) The Attempt at a...

Hi Everyone, I need to maximize \[Pi] = R*\[Alpha] (1/\[Alpha] (\[Beta]/R)^(1/( 1 - \[Beta])) - (1 - \[Gamma])*\[Beta]^(2/( 1 - \[Beta]))*\[Alpha]^(\[Beta]/( 1 - \[Beta]))) - (1/\[Alpha] (\[Beta]/R)^(1/( 1 - \[Beta])) - (1 - \[Gamma])*\[Beta]^(2/( 1 -...

Homework Statement A hardware store sells approximately 10 000 light bulbs a year. The owner wishes to determine how large an inventory of x (thousand) bulbs should be kept to minimize the cost for inventory. The carrying cost for the bulbs is $40/1000 while the paperwork for ordering is $12...

[SOLVED] Optimization Problem Homework Statement A tin can is to have a given capacity. Find the ratio of height to diameter if the amount of tin (total surface area) is a minimum. Homework Equations c=pi(r^2)h surface area = 2pi(r^2)+2h(pi)r The Attempt at a Solution h=...

[SOLVED] Optimization problem Homework Statement A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the smicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 28 feet? Homework...

Calculus: Optimization Problems Homework Statement Find the area of the largest rectangle that can be inscribed in the ellipse below. I'm not quite sure where to start...first of all, how would you even enter this into a calculator to graph? On the TI-83, I only see one variable 'x' that you...

Homework Statement I have been stuck working on this problem for the past little while and can't seem to figure it out. A construction company needs to create a trucking route for five years to transport ore from a mine site to a smelter. The smelter is located on a major highway 10km from...