# Tagged Questions

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

57 views

57 views

### What is the minimum point of $x\mapsto x^Ty$ for $|x|\le 1$ and a fixed $y\in\mathbb{R}^n$?

Let $y\in\mathbb{R}^n$. I want to minimize $$f(x):=x^Ty\;\;\;\text{for }|x|\le 1$$ The minimum point should be $$-\frac{y}{\sqrt{y^Ty}}\tag{1}$$ However, how can we derive $(1)$ analytically? Since $f$...
100 views

### General process to find global extrema of a function?

I have been reading and watching videos about local and global extrema, but all of this material covers the topic just graphically, and nobody really explicitly cares on how to find the global maximum ...
61 views

### Operations Resarch Optimal Scheduling

Consider the following problem: A car manufacturing company needs to transport car frames, which are $10$ cubic units each, and wheels, which are $2$ cubic units each, across the Atlantic ocean. ...
49 views

76 views

### How to find max value without Lagrange

I am trying to find the maximum and minimum values of the function $$f(x,y,z)=2x-y+4z$$ on the unit sphere $$x^2+y^2+z^2=1$$, but without using langrange multipliers or gradient. I would like to do ...
40 views

### Optimisation to solve for trigonometric expression?

I have a question that requires the use of optimisation to solve for the following expression: $$\cos ec{(\cos^{-1}{(-\frac{\sqrt{3}}{2})}+\sin^{-1}{(-\frac{\sqrt{3}}{2})})}$$ I'm a bit baffled, as ...
174 views

### Can I optimize area of cylinder with no givens?

I have a problem which should be very easy (as the rest of them are on this worksheet) but this one has me stumped. The question reads: A metal can is in the form of a cylinder. It has a bottom ...
86 views

### Fraction of area covered by three circles

Take a square with edges of size $10$. Now take take three circles of radius $5$. Prove that you can't cover the square with these three circles. Find the maximum proportion of the area of the ...
116 views

### Find $3$ numbers whose product is $27$ and whose sum is minimal

Find $3$ numbers whose product is $27$ and whose sum is minimal I'm thinking one might have to use langrange multipliers. The answer is $(3,3,3)$, I am not sure how to get there though.
2k views

77 views

### How to find $\theta$ at which $d$ is the maximum possible?

I have an equation: $$d=\dfrac{v\cos \theta}{g}\left(v \sin \theta + \sqrt{v^{2} \sin^{2}\theta + 2gh} \right),\ g≈9.81 \dfrac {m}{s^{2}}$$ How to find $\theta$ at which $d$ is the maximum possible?