Optimization Definition and 629 Threads

Homework Statement A farmer has 2400 feet of fencing and want to fence of a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area ? Homework Equations We wish to maximize the area A of the rectangle...

Hello. The problem is : I've got an expression to optimize with 7 free parameters. Ranges for each parameter are given. the simpliest way to optimize is to organize a program like for { for {for ...}} for each parameter and to get the result. Are there any other methods for solving the problem...

Homework Statement A rectangle is to be inscribed in a right triangle having sides 3 cm, 4 cm and 5 cm, as shown on the diagram. Find the dimensions of the rectangle with greatest possible area. Homework Equations 1. x^{2}+y^{2}=w^{2} in terms of w=\sqrt{x^{2}+y^{2}} 2...

Homework Statement The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the cost of running this ferry (labor...

How are Finding the max and min of a optimization problem different. and how do you distinguish them in an equation?

A police is flying at 150 mph at a constant altitude of .5 miles above a straight rode. The pilot uses radar to determine that an oncoming car is at a distance of exactly one mile from the helicopter, and that this distance is decreasing at 190 mph. Determine the speed of the car. This is a...

I'm really stuck on this problem. Could anyone provide some help? Find the length and width of the rectangle of largest area that can be inscribed in a semicircle of radius R, assuming that one side of the rectangle lies on the diameter of the semicircle. Also, find the area of this rectangle...

In this problem I have drawn out the region specified and noticed two sets of parallel lines indicating to me that a change of variable(u and v) are able to be used to solve this integral. I decided that u=y-x and v = -2x-y then solving for x and y I obtain x= (u-v)/3 and y = (4u-v)/3 From...

I am completely self taught in Calculus, but I would like to have a better understanding of it before I go to College. I was looking up problems and came across this: What is the distance d between the point A(2,-6,1) and the line l through B(3,4,-2) and C(7,-1,5)? I attempted this by finding 3...

Homework Statement Homework Equations The Attempt at a Solution For this problem, my group is having difficulty figuring out how much Styrene is reacting, since we don't know the molecular weight of polystyrene, we can't find the moles of polystyrene, which would be used to aid in finding the...

Homework Statement Assume a transmission imaging system with the following parameters: focal spot PSF equal to a Gaussian with FWHM = 0.5 mm, a detector PSF equal to a Gaussian with FWHM = 0.1 mm, source-to-detector distance = 100 cm. Compute: 1. the optimal source-to-object distance 2...

Homework Statement http://i.minus.com/jbkHm5oH1LfQ1k.png Homework Equations The area of a rectangle is its base times its height. The Attempt at a Solution The rectangle is inscribed. Its area is 2xy. I can substitute in the equation of the semicircle to get rid of the y-term...

Optimization - Why is there a constant term in the time equation?? Mod note: The OP apparently answered his own question. Homework Statement 1) A man can run at 8 km/hr and swim at 4 km/hr. He is currently 6 km from the shore of a lake, which is due east from him. He wants to get to a point...

Hi MHB, I've come across this problem recently: If a²+b²=2 and (c-3)²+(d-4)²=1, find the maximum value of ad-bc. I haven't solved it and actually, I don't know of any algebraic method I could use to solve it and I am wondering if this problem is doable with the Lagrange Multiplier...

So I am still confused about how to applying scaling of parameters to a general optimization problem. Let's say I am trying to do maximum likelihood estimation. I understand how to find the scaling matrix (assuming we restrict it to diagonal form) and that the Hessian should be close to the...

I am a physicist who is interested in acoustic guitar design (additionally I make custom made guitars and violins). The problem I have is in acoustic guitar design, for simplicity imagine a box 20"X15"X3" (length, width, depth). On one of the 20X15 surfaces (the top) cut a 3" hold 1/3 from...

I have a function z=f(x,y) that is reasonably well behaved (single global maximum). I can readily compute the value of z as well as partials of z with respect to x and y. I can also quite easily find the maximum. The challenge is to find the maximum and minimum values of x where c =...

Homework Statement Consider a power grid consisting of electricity producers that are connected to consumption points on the grid. The consumption points are affiliated with regional retail power companies that then distribute the power to their end users. The undirected graph (attached)...

I've just started programming with Python this summer, and I'm taking a course in computational physics this semester. I've been really enjoying it and programming in general, but I don't have much knowledge in computer science save for intro stuff (string/list methods, functions/classes...

Homework Statement Here is an alternative approach to handling absolute value terms as the decision variables: abs(x) is the smallest value z that satisfies x \leq z and -x \leq z. Using this,convert the following into a lp Min 2x1 + 3abs(x2) S.T x1 + x2 \geq 6 Homework Equations Here is a...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

I'd like 2 solve the following problem (well, routinely solve a bunch of such problems): Let us have a number of points (vertices), that can be interconnected. Not any 2 points are connected. Each connection is assigned a value. I want 2 find the maximum path in the graph, that is, the one with...

A simple vapor compression system. Based on constitutive relationships between pressure, temperature, enthalpy, etc., the system has four degrees of freedom. The two pressures in the system(p1 and p2), the level of superheat at the compressor outlet (T2) and the masss flow rate of the...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

I have a cost function which consists of sum of a set of quadratic loss plus a term which regularize function. my problem is: is there any way to infer probability from such a cost functions?

What exactly is "Engineering Optimization" I have the opportunity to take a grad class entitled "Engineering Design Optimization" this fall and I am curious about the subject. I have never taken an optimization class before and to be honest I don't quite understand why optimization is...

The equation for heat transfer is: 1. Q = U.A.(TL-T1) Where: Q= heat transferred (W). U= overal h.t. coefficient. A= area of heat exhanger (m^2). TL= Temp. of refrigerated space (Kelvin) T1= Low temp. of refrigerant= refrigerant in evaporator (K) I want to eventually find the maximum heat...

Suppose you have two poles separated by the distance $w$, the first of height $h_1$ and the second of $h_2$, where $0<h_1<h_2$. You wish to attach two wires to the ground in between the poles, one to the top of each pole, such that the angle subtended by the two wires is a maximum. What portion...

Hey Everyone, I'm having trouble setting up this word problem. I know that area of a circle is pir2 and area of a triangle is 1/2bh but for some reason I can't find a way to combine these equation together. What are the radius and area of the circle of maximum area that can be inscribed in an...

Here are the questions: I have posted a link to this topic so the OP can see my work.

Here is the question: I have posted a link there so the OP can see my work.

θHomework Statement The attached diagram depicts a sphere with several variables: the height of the cylinder, the radius of the cylinder and an angle. All that has been given to me is the hypotenuse of a triangle used. Homework Equations To my knowledge I was told to use 2sinθcosθ=sin2θ...

First refer to this question:Is this function "$h$" symmetric of the plane $x=y$? - Mathematics Stack ExchangeThe main problem is to find an appropriate (objective) function (a curve) to compare the implicit filtering method and Nelder-Mead method for optimization. The backgrounds of these...

Hi context: The USD/CNH currency pair has been trending down at an almost linear rate past 3 years, it's safe to assume it will continue to trend downwards for the short term foreseeable future as the Chinese govt slowly allows the Yuan to appreciate to its real value. The problem: Every...

The problem is posted here: http://nrich.maths.org/5673 I tried subbing in values to get the biggest area: perimeter ratio possible. I used an arbitrary value, 12, for perimeter. For the triangle, I took out the hypotenuse and so A = 1/2(x)(y) where x+ y = 12. Its area is biggest when x = y = 6...

Homework Statement The link to the problem is here: http://i.imgur.com/wyOsoSB.png The Attempt at a Solution I'm not completely sure about my work so far so please bear with me. My professor is very poor at professing the subject so I'm trying to learn from the book. Please let me know...

Homework Statement Find the maximum point of P(h)=-10h+4410-(6800/h) Homework Equations P(h)=-10h+4410-(6800/h) The Attempt at a Solution P(h)=-10h+4410-(6800/h) P'(h)=-10+(6800/h^2) P'(0)=-10h^2+6800 10h^2=6800 Divide both sides by 10: h^2=680 and sqrt both sides: h=26.1

Here is the question: Here is a link to the question: CALCULUS needHELP WITH THIS PLEASE! APPRECIAT EIT -? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Joe is traveling from point A across a circular lake to a cabin on the other side at point B. The straight line distance from A to B is 3 miles and is the diameter of the lake. He travels in a canoe on a straight line from A to C. She then takes the circular trail from C to...

Homework Statement Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Homework Equations The Attempt at a Solution let a,b represent the two non negative numbers a=x b=30-x So, x^2+(30-x)^2=s, where...

Homework Statement Homework Equations The Attempt at a Solution I am not really sure how to optimize it from here. What should I be taking the derivative of the price function with respect to ??

1. A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is (a) a maximum? (b) A minimum? 2. A_{s}(x) = x^{2}, A_{t}(x)=\frac{\sqrt{3}}{4}x^{2}...

Homework Statement The question is: Suppose that lim x_k=x_*, where x_* is a local minimizer of the nonlinear function f. Assume that \triangledown^2 f(x_*) is symmetric positive definite. Prove that the sequence \left \{ f(x_k)-f(x_*) \right \} converges linearly if and only if \left...

The question is:Suppose that lim $x_k=x_*$, where $x_*$ is a local minimizer of the nonlinear function $f$. Assume that $\triangledown^2 f(x_*)$ is symmetric positive definite. Prove that the sequence $\left \{ f(x_k)-f(x_*) \right \}$ converges linearly if and only if $\left \{ ||x_k-x_*||...

Homework Statement We want to make a conical drinking cup out of paper. It should hold exactly 100 cubic inches of water. Find the dimensions of a cup of this type that minimizes the surface area. Homework Equations SA = pi*r^2 + pi*r*l where l is the slant height of the cone. V =...

Here is the question: Here is a link to the question: Calculus Max Min problem help? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: I need help on a HW problem - I got the first two parts right, but am having trouble finishing the last two? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Calculate biggest and lowest value to function f(x,y)=x^5y^4e^{-3x-3y} In the triangle has vertices in points \left(0,0 \right),\left(6,0 \right) and \left(0,6 \right) Before I start I want to warn that I used google translate in the text 'In the triangle has vertices in points' Progress: I...

Here is the question: Here is a link to the question: Show that the minimum and maximum points for y=f(x) occur among the min and max points for y=f^2(x).? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: Helpppppppppppp please !? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.