What is Optimisation: Definition and 72 Discussions
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.
Homework Statement
Find the trapezoid of largest area that can be inscribed in a semicircle of radius a, with one base lying along the diameter.
Homework Equations
diameter = 2a
area of a semicircle = (1/2)πr2
area of a trapezoid = (1/2)(b1 + b2)h
The Attempt at a Solution
so...
An orchardist has one grove of 50 orange trees. Each tree produces 800 oranges. The orchardist knows from experience that each addition tree planted in the grove will reduce the output of each tree by .10 oranges. How many tree should the orchardist plant in the grove in order to maximize the...
A manufacturer can sell x CD players per week at d dollars per item, where
x = 600 - 3d
Production costs (in dollars) are given by:
C(x) = 600 + 10x + 0.4x2
How should the CD players be priced in order to maximise profits?
------------
I have tried a variety of ways but...
A rectangular parcel with square ends is tied up with string, which passes once around the parcel lengthwise and once crosswise. If the volume of the parcel is 2322m3, find its dimensions if the length of string used to tie it is to be minimised.
V = lwh = 2322
Let D be the dimensions...
Hello physics forum, can someone please explain to me the thought process that one uses to solve a question like this?
A leak has been discovered in a water supply pipe that will take several days to repair. Suppose that it is leaking at a rate given by the function 4 + 0.2t, that is...
Hello
I have a function which is very similar in shape to a Gaussian, except it is not a distribution and it is not analytic, so I can at best calculate a single point on the curve at a time. (In general it is a convolution of different distributions but this is not important).
I need to find...
Hello
I am trying to speed up a code which performs a number of tasks on a set of data. I am wondering if there are any resources on general rules and principles that can be used to speed up calculation times?
I am having a real problem when there appear to be more than one way to code...
Homework Statement
Basically i have a minimize a least square function, and my function depends on three variables a,b,c and constraints a>=0, b>=c>=0 . I assigned initial values, minimum and maximum boundary limits for a,b &c.
Homework Equations
I have a problem in executing the...
Quick question,
I am taking this analog design class and the class includes a project which requires design optimisation using either excel,or mathcad
Has anyone used excel to optimise the design?
If yes, can you please guide me to the resource on how to setup excel to optimise or give...
http://img119.imageshack.us/img119/3906/optdp4.th.jpg
http://img246.imageshack.us/img246/7067/opt1rf0.th.jpg See two attached files for the problem and markscheme
My question is, why must one differentiate in part d; the markscheme finds dS/da and then says the function is increasing, before...
for the problem:
- find H and W as functions of y0, E (having a method to solve for y0 = const, E=const is fine, too) such as product HW is max, under constraint: HW/(y0 + H) < E
if numeric, the method should be fast.
any suggestions?
hello ,i m quite new to Matlab and I am sorry if my question is too trivial but i couldn't find answers in help.Im trying to solve an optimisation problem .given the execution time for different tasks(sorting algorithms),i plotted the cumulative distribution functions.(y axis-cumulative...
Hi, I'm relatively new to this forum but i hope you will be able to help me with my maths problems.
Problem1.) An ant is at one corner of a cube side length one unit. the ant needs to get from his corner to the corner on the opposite side of the cube (at the top of the cube not the bottom) he...
Hi, I'm relatively new to this forum but i hope you will be able to help me with my maths problems.
Problem1.) An ant is at one corner of a cube side length one unit. the ant needs to get from his corner to the corner on the opposite side of the cube (at the top of the cube not the bottom) he...
Homework Statement
A right angled triangle with sides of length a, b and 2r is trapped within a semi-circle of fixed radius r. Given that all three vertices are on the semi-circle, find the values of a and b that will maximise the area of the triangle...
Homework Statement
The first problem is a related rates question:
A swimming pool if 5m wide and 25m long, 1m deep at the shallow end and 4.5 deep at the deepest point. A cross section is shown in the figure below. The pool is being filled at a rate 0.5m^3/hr. Use calculus techniques to...
Hello,
I would be interrested to learn if there are some (new) open source and/or possibly free librairies available for nonlinear optimisation and equations solving.
I would be mostly interrested in modern languages like java or C# . "Clean" fortran could also be interresting as long as...
Hello,
I would be interrested to learn if there are some (new) open source and/or possibly free librairies available for nonlinear optimisation and equations solving.
I would be mostly interrested in modern languages like java or C# . "Clean" fortran could also be interresting as long as...
Hey
I am given the set volume for a cylindrical container and separating pricing for the material used to construct the container, the base and the side wall. The ends of the container cost $0.05 per cm2 and the side walls $0.04 cm2, and the volume is 400 mL. The question asks: What is the best...
G'day guys, got this question out of Step-by-step calculs by J.G. graham for those of you who have the book.
I've had quite a bit of a play around with it but it doesn't seem to be going anywhere i end up with a few equations which have 3 variables, and i can't reduce it to two.
Okay...
I have been given a problem of taking an object (I used a Cornflakes Box) and finding the optimal surface area compared to its volume (volume and ratio between sides constant)
I got:
Cornflakes Box :
Length = 25cm
Height = 36 cm
Width = 9 cm
Optimal Surface area box:
Length = 17.3...