Optimization Definition and 588 Threads

The problem: Relevant Equations: A = l * w So I drew a rectangle like this: And I'm not really sure how to proceed from this point.. I always have a hard time setting up the problems for optimization :/ Any tips to the right direction would be greatly appreciated! Just to clarify, this is...

Homework Statement Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 4. Solve by writing the area as a function of θ Homework Equations A=1/2 (bh) The Attempt at a Solution Given the side h and the hypotenuse 4, we can find the base of the smallest...

Find the minimum of $\sqrt{a^2-12a+40}+\sqrt{b^2-8b+20}+\sqrt{a^2+b^2}$.

Friends, I want to know the methods involving the airfoil design and optimization. from initial step onwards...how to start my works.

Find the maximum value of the function $\sqrt{x^4-9x^2-12x+61}-\sqrt{x^4-x^2+1}$.

I would like to ask for help solving this problem. I've been at this problem for a few hours without making any progress. There is a picture of the problem attached in this thread. So, the question is what is the length of side 'X' used in order to get the shortest possible length for side...

[Note: Post restored from archive - gneill, PF Mentor] Homework Statement A pendulum consists of a uniform circular disk of radius r which is free to turn about a horizontal axis perpendicular to it's plane. Find the position of the axis for which the periodic time ( for small amplitude...

Hey guys! I need a little help in continuing my research i did this summer. So a little background information: This summer i conducted research at a REU where i focused on optimizing the power output of a wind farm by modeling wind turbine locations within a constrained space. I wrote a...

Hey guys, I'm having trouble with this problem set I'm working on at the moment. I'd appreciate some help with this question: (I'm only asking about number two. Ignore number one please.) So if the length for the hypotenuse of the leftmost triangle is represented by: c^2 = x^2 + y^2 Then...

Find the maximum of $P(x)=\dfrac{x(\sqrt{100-x^2}+\sqrt{81-x^2})}{2}$.

I recently noticed that I have blindly used optimization in some problems that involve symmetrical insulating/conducting spheres and cylindrical shells. For example, when calculating outer electric field caused by a spherical insulator/conductor, I just treated these as a simple point charge...

Homework Statement Find the first-octant point P(x,y,z) on the surface closest to the given fixed point Q (0,0,0). The surface x2y2z=4 Homework Equations is the distance along PQ. EDIT: The Attempt at a Solution I get stuck here every time. I feel like I'm just selling myself...

Dear physicist, I am designing a device that will use firetruck/hydrant water pressure (~150 psi) and fire hose (5" diameter) to lift up a device in the air and into a burning room. Please advice me and help understand how water flow, pressure and areas influence thrust. My goal is to input...

Homework Statement Just a heads up, this is a problem with parts (a) - (o). I am working on (k). I am working on problem 5 in the attached PDF. I will show my code for the other parts. We were told to use N = 5 while writing the code for debugging and testing, but run N = 500 for the real...

I' at a a very very very basic level of calculus and usually have to watch a video or read something basic just to understand the basics. I'm fascinated by optimization equations, for example what is the largest area that can made with 500m of fencing. So at some point in solving this we end...

My Goal: to find what fraction of my monthly payment should go to each loan. The ideal outcome would be to pay the debt as fast as possible. I have several loans, but for now, I want to start with a simple exercise of one loan that accrues monthly interest and one fixed monthly payment for that...

Hey all, I'm working on the JUICE mission (Jupiter Icy Moons Explorer) and I've been tasked with finding software (preferably open source, but paid is fine) that can optimize circuit network designs that I upload. Originally I was trying to find programs that would run optimization using the...

I have the summation (from i=0 to n) of (F_{t})(R) / (1+d)^i where F_{t} = (F_{t-1})[(R)(I_{p}) +(1-R)(I_{r})] (The F_{t-1} is referring to the value of F in the last period) I want to find the value of R that maximizes the summation. So must I take the partial derivative wrt R? How do I...

Hello all, I am trying to solve this problem, and I don't know which way to go... The product of the maximum value and minimum value of the function: \[z=e^{x+2y}\] under the condition: \[x^{2}+y^{2}=5\] Equals to: a. 0 b. 1 c. e^5 d. e e. e^-1 I have a feeling that this problem involves...

Error running optimization. Inputs must be a scalar and a square matri I am trying to use fminunc using optimtool. But i got the error Error running optimization. Inputs must be a scalar and a square matrix. this is the function i typed in the editor. function F = fun(x) F =...

For my B.Eng project, I'm optimizing the thermal efficiency of a boiler using genetic algorithm in MATLAB. I'm finding it very tough to write my fitness function, constraint equations and upload my initial population which is a set of data from my case study plant. for boiler thermal...

These 2 questions,I have attempted them for hours but still no outcome:confused: For the first question: part a) i take the ∇f(x) and set it to be zero; then find out(x1,x2)=(0,-1) or((-2a-1)/3,(-2a-4)/3); but then for part b), after using second-order necessary condition, i have no idea...

A student in hs I tutor was giving the following problem: Maximizes the volume of a cylinder inscribe in a sphere of radius 6. We worked through it and had: \begin{align} h &= 2(6 - x)\\ r_{\text{cylinder}}^2 &= x(12 - x) \end{align} Now the volume of a right cylinder is \(V = \pi r^2h\) so \[...

Here is the question: I have posted a link there to this thread so the OP can view my work.

There is a large chunk of information necessary as a preface to my question, so bare with me for a paragraph or two. I work for a pond treatment company. We have a set number of ponds we treat during a month, some are contracted to be treated once a month, some are treated twice. The question is...

Been a while since I stopped by here... There's one thing about optimization on non-compact sets that's been bugging me for quite a while and I'd love to hear how you perceive things. Say we are optimizing a partially differentiable (and thus continuous) function $f:\mathbb{R^2} \to...

Homework Statement There are n amount of wi-fi networks in a given neighborhood. For every pair that are within 50 yards, the frequency used must be different, otherwise there will be interference. How few frequencies are required so that every wi-fi network can be assigned a frequency without...

Im having trouble starting the harder optimization problems in stewarts calculus (calculus 1). I noticed one of my major problems is not knowing how the picture of the optimized problem looks like. My test is only going to contain one optimization problem. So I am not worried about failing...

Here is the question: I have posted a link there to this thread so the OP can view my work.

If the sum of the surfaces of a cube and a sphere as is constant, deierminar the minion of the diameter of the sphere to the edge of the cube in cases in which: 272) The sum of the volumes is minimal 273) The sum of the volumes is maximum And the answer are 272 = 1 and 273 = infinit Ok Vs =...

Wasn't sure whether to post this in the computing section or not but here goes anyway, I have n number of 2d vectors (all have the same magnitude), for each vector I can choose whether or not to multiply it by -1 (spinning it through 180 degrees), all of the vectors are then added together, The...

Hi, I have a optimization problem and I need to find a way to solve it even if only with an approximate solution. Let's suppose we have a finite set of vertical containers each with a distinct liquid chemical inside.(say a handful of vertical pipes). At the top, these containers have an...

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

Hi guys, I'm a bit rusty on optimization, but i remember enough to be able to setup some problems that I am facing in my research, and would like to know how to go about solving such problems in general. The equations below may have more variables and be in slightly different forms at times...

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

Here is the question: I have posted a link there to this thread so the OP can view my work.

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...

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...