Optimization Definition and 588 Threads

Heres what i did for this one. find an equation relating work + math = 16 (total hours she has in a day). so math = 16 - work (i plug that into the equation for h) and for money, i have y = 6*work + 6 i plug this in as well and take the derivative. i get f ' = -4/3 *(6worrk + 6)^-2/3...

Prove that any cylindrical can of volume K cubic units that is to be made using a minimum of material must have the height equal to the diameter.

Hello, I am having a little trouble understanding what the question is asking so I was hoping someone would be able to clear up the language the textbook uses. Thanks! A piece of window framing material is 6m long. A carpenter wants to build a frame for a rural gothic style window where...

Q: A trough is to be made from three planks, each 12 in. wide. If the cross section has the shape of a trapezoid, how far apart should the tops of the sides be placed to give the trough maximum carrying capacity? OK the area of a trapezoid is A=2bh I know that much, but I've been...

Q: A solid if formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 12 cm^3. Find the radius of the cylinder that produces the minimum surface area. OK, I got about halfway through my problem before I got lost. V of shpere= 4/3(pi)r^3...

(See Attachment) I don't quite understand what i am supposed to optimize, and what my restriction formula is. Is QT constant? But in that case, how could i optimize PRS? I tried the following: l = PR + RS PR^2 = PQ^2 + QR^2 cos\theta1= \frac{QR}{PR} PR = \frac{QR}{cos\theta1} Similarly...

Question #1 A printed page will have margins of 2 cm at the top and sides and 4 cm at the bottom. If the printed area is 150cm squared, find the dimentions of the whole page so that its area will be a minimum. Question #2 Painters are painting the second floor exterior wall of the building...

Question: [ A rectangular box, whose edges are parallel to the coordinate axes, is inscribed in the ellipsoid 96x^2 + 4y^2 + 4z^2 = 36, What is the greatest possible volume for such a box ] I realize that the volume of the box: V = (2x)(2y)(2z) = 8xyz Thus far I've solved for z^2 in the...

Is anyone willing to check my solution to this problem? The problem is described on part 1 of the solution. http://img458.imageshack.us/img458/5418/solution016dj.jpg" http://img458.imageshack.us/img458/7669/solution025zk.jpg" http://img458.imageshack.us/img458/6652/solution030fr.jpg"...

I am having trouble setting up the primary equation to this optimization problem. Here is a link to the problem http://img293.imageshack.us/img293/806/appliedminmaxprob5vo.jpg" Here is the best equation I can come up with but this leads me nowhere... The hypotenuse of the each...

Hi, I have the following problem of Calculus I class... I don't understand it and I don't know how to resolve it, can anybody help me?? A farmer wants to fence an area of 1.5x10^6 ft^2 in a rectangular field and then divide it to the half with a parallel fence at one side of the rectangle...

If an open box has a square base and volume of 108 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. :confused: don't even know where to start on this problem.

I was wondering if someone could workout this problem... The sum of the perimeters of an equilateral triangle and square is 10. Find the dimensions of the triangle and the square that produce a minimum total area. Thanks for any help

OK, here is the situation. I am supposed to write optimization code in Matlab to determine which of two missions an airplane should perform. There are three total, but one of them has been decided on. So I need to determine which of the other two I should do. The problem is that I have...

hi, what i am trying to do is maximize the sum of distances to the power alpha between all the points D_{\alpha} (\mathcal{U}) = \sum_{i=1}^m \sum_{\substack{j=1\\j\neq i}}^m|\mathbf{u}_i - \mathbf{u}_j|^\alpha on the surface of a sphere of radius 1 where \mathbf{u} \in \mathbb{R}^3 and...

Problem: An open top box is constructed from a sheet of material by cutting equal squares from each corner and folding up the edges. If the sheet of material measures 14 inches by 9 inches, find the dimension x which represents the length of one side of the square that should be cut off so that...

Minimizing Construction Costs: If an open box has a square base and a volume of 108 in.^3, and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. This is what I have so far: Volume: 4y^3-4xy^2+x^2y=1=108...

The sum of two nonnegative numbers is 20. Find the numbers if a. the sum of their squares is as large as possible; as small as possible b. one number plus the square root of the other is as large as possible; as small as possible. a. x+y = 20 x^2 +y^2 = N (20-y)^2 + y^2 = N -40 +...

I have a really tough question and need like emergency help and aid... a juice manufacturer is studying the most economical shape to use for a beverage container. Each unit will contain 335cm^3 of juice. The manufacturer is considering a cylinder versus a rectangular prism with a comfortable...

optimization problem! OKOK running out of time! CAn anyone please help me with this problem: Surface Area A solid os formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 12 cubic centimeters. Find the radiusof the cylinder that...

I have couple of questions on optimization, i don't want the answer, i just want to know what i have to do to approach this question. Keep in mind that I am in grade 12 calculus, i.e. PLEASE don't give me some crazy university answer with equations I've never seen before. Anyways, here are the...

I've used differentiation to find that a rectangular enclosure made up of a 100m fence should have four sides all 25m to be as large as possible. The function I get is 50x-x^2. As I said, differentiating this function gives me the largest area possible. But how would I go about finding how long...

Optimization Problems (So confusing) Please me on this once. Thanks in a million ! The Dome Tent 1 .Imagine making a tent in the shape of a spherical cap (a sphere with lower portion sliced away by a plane). Assume we want the volume to be 2.2 m^3, to sleep two or three people. a. make a...

a landscape architect plans to enclose a 3000 square foot rectangular region in a botanical garden. She will use shrubs costing $25 per foot along three sides and fencing costing $10 per foot along the fourth side. Find the minimum total cost. I started off this problem by finding the length...

Help -- Optimization Problem Hello people, I am working on certain energy optimization problems in multiprocessor systems. My objective function is: E= U*x / (1-yC)^2 where U and C are constants and x and y are independent variables. I need to minimize this function under the constrain...

I have two questions. A) Show the parallelipided with fixed surface area and maximum volume is a cube. I've already proven that we can narrow down the proof to a box. So, basically, I'm really lost on how do prove that a cube is the box with a fixed surface area and maximum volume. B)...

How to find a positive number such that the sum of the number and its reciprocal is as small as possible ?

A choclate manufacturer uses an equilateral trianglular prism package. if the volume of chocklate to be contained in the package is 400 cm ^3 . what dimenesions of the package will use the minumum amount of materials? i'm having trouble putting the formulas together, I am thinking of the...

A woman at a point A on the shore of a circular lake with a radius of 2 miles wants to arrive at the point C opposite A on the other side of the lake in the shortest possible time. She can walk at a rate of 4 miles an hour and row a boat at 2 miles an hour. How should she proceed...

Optimization: I am going insane here :cry: :cry: I've really run out of ideas... please help me.! %golden.m function [f,a]=golden(func,p,tol) func='dfunc'; p=[0 1] g=0.38; a=p(1); b=p(2); r=b-a tol=0.01; iter=0 while r>tol x=[a+g*r b-g*r] y=feval(func,x) if...

Hi, I just needed help starting off this problem: "A 1-km racetrack is to be built with two straight sides and semicricles at the ends. Find the dimensions of the track that encloses the maximum area." There was a similar question which I did before this which involved a Norman...

is there a good website on how to do optimization online?? we learning this section now in our calc class but our teacher didn't really explain anything, he only did one example and told us the rest were all similar but i din't know where to even begin on some of then... #2. A company must...

hi i have two homework assignment I'm kinda stuck on they are very similar i was hoping someone could help me... 1) A rancher wants to fence in an area of 1,900,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the...

This is homework (forgive me) but I don’t want an answer I would just like to know what I am doing wrong. Here is the problem: Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3cm and 4cm if tow dies of the rectangle lie along the legs...

I have a semi-project due tommorrow that basically asks the following question: If you are designing a tent in the shape of a spherical cap (a sphere with the lower portion sliced away by a plane) and the material used for the roof costs 2.5 times more per square foot than the material used for...

Find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 12-x^2

What is the area of the largest rectangle that can be inscribes indiside a semicircle with the radius r? answer: x = r / SQRT(2) A = r^2

[SOLVED] Optimization Using Differentiation I have an assignment in which we are to optimize problems using a given 6-step process. More or less it involves Max/Min differentiation. On of the problems are as follow; Enclosing the Largest Area The owner of the Rancho Los Feliz has 3000 yd...