 # Unleash Your Optimization Potential with Expert Support and Comprehensive Practice

Recent questions in Optimization Brooke Richard 2022-11-09

## A square and a equilateral triangle are to be formed out of the same piece of wire. The wire is 6 inches long. How do you maximize the total area the square and the triangle contain? Adison Rogers 2022-11-04

## How do you find the dimensions of a rectangle whose area is 100 square meters and whose perimeter is a minimum? Stephany Wilkins 2022-10-27

## How do you find two positive numbers whose sum is 300 and whose product is a maximum? Paloma Sanford 2022-10-23

## Let $V={R}^{d}$ and $\left({x}_{i},{y}_{i}{\right)}_{1\le i\le n}\in \left(V×\left\{-1,1\right\}{\right)}^{n}$Let $C=\left\{\left(w,b\right)\in V×R:1-{y}_{i}\left({w}^{t}{x}_{i}-b\right)\le 0,\mathrm{\forall }i\in \left[1,n\right]\right\}$Show that $mi{n}_{\left(w,b\right)\in C}||w|{|}^{2}$ has a solution $\left(w,b\right)$What I tried:$||w|{|}^{2}$ is clearly continuous, I proved that C is closed. If C is bounded, then C is compact and the solution exists (In this case, I don't know how to prove that C is bounded). If C is not bounded, I don't know how to conclude either. Keyla Koch 2022-10-21

## How do you find the largest possible area for a rectangle inscribed in a circle of radius 4? Bairaxx 2022-10-18

## A rectangular box is to be inscribed inside the ellipsoid $2{x}^{2}+{y}^{2}+4{z}^{2}=12$. How do you find the largest possible volume for the box? Amina Richards 2022-10-13

## How do you optimize $f\left(x,y\right)=2{x}^{2}+3{y}^{2}-4x-5$ subject to ${x}^{2}+{y}^{2}=81$? Damon Vazquez 2022-10-06

## How do you find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum? Nathanael Perkins 2022-09-27

## How do you find the dimensions of the box that minimize the total cost of materials used if a rectangular milk carton box of width w, length l, and height h holds 534 cubic cm of milk and the sides of the box cost 4 cents per square cm and the top and bottom cost 8 cents per square cm? Vrbljanovwu 2022-09-27

## What is the maximum possible area of the rectangle that is to be inscribed in a semicircle of radius 8? Addyson Bright 2022-09-24

## Consider a NLP $min\left\{f\left(x\right):g\left(x\right)\le 0\right\}$. There are no equality constraints. The problem is feasible for small steps $t>0$. I have to prove that $g\left(x+td\right)\le 0$ if $g\left(x\right)<0$, where $t$ is the step length and $d$ is the direction of the line search (gradient descent).I was thinking that since $t$ is positive and the direction $d$ can not be negative (not too sure about this fact), hence their multiplication is positive. The only way for $g\left(x+td\right)$ to be 0 or negative is for $g\left(x\right)$ to be negative. ct1a2n4k 2022-09-23

## How do you find the length and width of a rectangle whose area is 900 square meters and whose perimeter is a minimum? Thordiswl 2022-09-23

## 1- What is Optimization? How many methods are there to calculate it?2- What do we mean by an objective function? What do we mean by constraints?3- Give three practical examples (physical or engineering) of a target function with a constraint koraby2bc 2022-09-23

## What are the radius, length and volume of the largest cylindrical package that may be sent using a parcel delivery service that will deliver a package only if the length plus the girth (distance around) does not exceed 108 inches? Linda Peters 2022-09-20

## The productivity of a company during the day is given by $Q\left(t\right)=-{t}^{3}+9{t}^{2}+12t$ at time t minutes after 8 o'clock in the morning. At what time is the company most productive? hotonglamoz 2022-09-20

## How do you find the points on the parabola $2x={y}^{2}$ that are closest to the point (3,0)? Keenan Conway 2022-09-19

## I have a knapsack problem$\begin{array}{rl}& \underset{x\in \left\{0,1{\right\}}^{n}}{max}\sum _{i=1}^{n}{v}_{i}{x}_{i}\\ & \text{s.t.}\sum _{i=1}^{n}{w}_{i}{x}_{i}\le c.\end{array}$The Lagrangian relaxation is as follows$\begin{array}{r}\underset{\lambda \ge 0}{min}\underset{x\in \left\{0,1{\right\}}^{n}}{max}\sum _{i=1}^{n}{v}_{i}{x}_{i}-\lambda \left(\sum _{i=1}^{n}{w}_{i}{x}_{i}-c\right).\end{array}$Suppose I solved the relaxed problem and got an optimal ${x}_{lag}$ s.t. $f\left({x}^{\ast }\right) where ${x}^{\ast }$ is the optimal solution of the original problem and $f$ is the objective function. Even though ${x}_{lag}$ gives a strict bound, is it consideblack to be a good approximate solution?Is it true that the relaxation can be solved in polynomial time since the dual problem is convex in $\lambda$ and the maximization part with fixed $\lambda$ is just activating ${x}_{i}$ associated with the largest term $\left({v}_{i}-\lambda {w}_{i}\right)$? unjulpild9b 2022-09-17

## A cylindrical can is to be made to hold 1000cm^3 of oil. How do you find the dimensions that will minimize the cost of metal to manufacture the can? overrated3245w 2022-09-07
## What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 125 $c{m}^{3}$? Ariel Wilkinson 2022-09-06