91 Answered Questions for the topic Optimization

Find the area of the largest isosceles triangle that can be inscribed in a circle of radius r = 14 (see figure).

Solve for the area, and write as a function of h and then as a function of a.

12/06/19

Optimization Calculus Question

An industrial tank is formed by adjoining two hemispheres to the ends of a right circular cylinder.  The tank must have a volume of 4000 cubic feet.  The material for the lateral surface costs $5... more

12/04/19

Optimization and Related Rates problem

This question uses the inverse-square law, which states that the light intensity experienced at a distance x from a light source is proportional to the luminosity of the source times x^(-2).It is... more

12/04/19

Optimization and Related Rates problem

This question uses the inverse-square law, which states that the light intensity experienced at a distance x from a light source is proportional to the luminosity of the source times x^(-2).It is... more

06/19/19

Fastest way to get sign in Java?

I'd like to get the sign of a `float` value as an `int` value of -1 or 1. Avoiding conditionals is always a good idea in reducing computational cost. For instance, one way I can think of would be... more

05/29/19

How do I check if cartesian coordinates make up a rectangle efficiently?

The situation is as follows: - There are N arrays. - In each array (0..N-1) there are (x,y) tuples (cartesian coordinates) stored - The length of each array can be different I want to extract the... more

05/27/19

Tuning and optimizing a MATLAB/Simulink Model?

I would like to optimize output signals, by tuning some of the input parameters with ease (preferably in real-time) by looping the simulation of the model again and again at a speed where the speed... more

04/25/19

120 feet of fencing to enclose 3 adjacent corrals

We have 120 feet of fencing to enclose three adjacent rectangular corrals with one side against a wall. Find the dimensions of the rectangles whose area is as large as possible.

03/22/19

How to know whether Lagrange multipliers gives maximum or minimum?

My book tells me that of the solutions to the Lagrange system, the smallest is the minimum of the function given the constraint and the largest is the maximum given that one actually exists. But... more

03/21/19

How to know whether Lagrange multipliers gives maximum or minimum?

My book tells me that of the solutions to the Lagrange system, the smallest is the minimum of the function given the constraint and the largest is the maximum given that one actually exists. But... more

03/15/19

How to know whether Lagrange multipliers gives maximum or minimum?

My book tells me that of the solutions to the Lagrange system, the smallest is the minimum of the function given the constraint and the largest is the maximum given that one actually exists. But... more

03/14/19

Why does a distance and its square reach their minimum at the same point?

There is a question in my calculus textbook that asks to find a point on the parabola $y^2 = 2x$ that is closest to point $(1,4)$. They want us to first use the distance formula, but then... more

02/19/19

optimization question

Maximize the volume of a rectangular prism whose base area is given by the polynomial 36+15x-3x^2 and whose height is 20x-90.

02/19/19

optimization please help

A luxury hotel group purchases a deserted island 3. 5 miles offshore and due south of an endangered bird nesting beach. The nearest power source is on land, 10 miles due east of the bird nesting... more

11/17/18

Optimization Problem

A box is contructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $3 per square foot and the metal for the sides costs $8 per square foot. Find... more

11/13/18

Finding the dimensions of a rectangle with max area that can be in a circle

Find the dimensions of a rectangle with the max area that can be inscribed in a circle of radius 10.

10/05/18

How do you find points given the following?

Find the points on the graph of the function that are closest to the given point.f(x) = x^2,(0, 9)

07/03/18

Very confusing optimization question!

I am really confused about this equation and how do you derive the volume and area equation! ” An open-top rectangular box is to be 6 meters high and have a volume of 300 cubic meter. Find the... more

06/21/18

Charlie has an 8m plank. He plans to cut it into 4 pieces to make a rectangular sandbox. Show that he can maximize the area of the sandbox by using a square

I don't know what to do here ??? please help   Continuation to question- with a side length of 2m

05/13/18

What size square should be cut out to create a box with greatest volume? What is the maximum volume?

An open box is to be made from a piece of plastic 20 by 20 inches by cutting out squares of equal size from the corners and bending up the sizes. 

04/17/18

how to find an equation that links the minimum surface area given a certain volume

a diving tank manufacturer is trying to reduce costs of its manufacturing process by reducing the amount of material that is used to produce their tanks. They came to you for consultation as to how... more

04/02/18

Find the dimensions x and y of the rectangle of maximum area that can be formed from a 100-in. piece of wire.

Find the constraint and solve for y.Find a formula for the area in terms of x alone.What is the interval of optimization?Maximum area is

04/01/18

find the dimensions of the can (radius and height) that will minimize the amount of material used (surface area)

a cylindrical soda can is being designed to hold a volume of approximately 23.56 in3
1 3 4

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