# Optimisation and best use of space

• jendrix
In summary, the diagram is too small to read the dimensions of the concert venue, so I can't figure out what the problem statement is. I've solved it to the best of my ability, but the final question I'm stuck on asks to critically examine the shape of the concert venue with this maximum area and comment on it.Make 2 suggestions for improving the concert venue given that the perimeter must remain the same.
jendrix

## Homework Statement

I initially had to use the attached diagram to solve problems related to a concert venue.So I created a formula for perimeter and area and used these to create a formula for area with x as the only variable.I used differentiation to find the value of x when the area is at a maximum.

Value for Pi given as 22/7

P=4xy + 2x +Pix

A=4xy +Pix^2/2

y=p-36/7x

y into area formula to give a= px -25x^2/7

The final question I'm stuck on asks "Critically examine the shape of the concert venue with this maximum area and comment on it.Make 2 suggestions for improving the concert venue given that the perimeter must remain the same"

## Homework Equations

I've solved these to

a =-25x^2/7 + px and x =7p/50

## The Attempt at a Solution

I'm a little stuck on what the final question is asking, my intial observations are that a circle would give the maximum area based off a fixed perimeter and that while a square offers more area than a rectangle, now it is used in conjunction with a semi-circle the rectangle provides the best solution.As the circle is linked to the x value, if you reduce x to make a square the area of the circle is reduced.

Last edited:
jendrix said:

## Homework Statement

I initially had to use the attached diagram to solve problems related to a concert venue.So I created a formula for perimeter and area and used these to create a formula for area with x as the only variable.I used differentiation to find the value of x when the area is at a maximum.

The final question I'm stuck on asks to critically examine the shape of the concert venue with this maximum area and comment on it.Make 2 suggestions for improving the concert venue given that the perimeter must remain the same.

## Homework Equations

I've solved these to

a =-25x^2/7 + px and x =7p/50

## The Attempt at a Solution

I'm a little stuck on what the final question is asking, my intial observations are that a circle would give the maximum area based off a fixed perimeter and that while a square offers more area than a rectangle, now it is used in conjunction with a semi-circle the rectangle provides the best solution.

Your diagram is so small that I can't read the dimensions on it. Please provide the exact problem statement, including the dimensions of the concert venue.

So I'm thinking of covering the below in my obeservation:

How and circle or square are usually the best use of perimeter for maximum area with proven examples in the form of equations.

How in this example this doesn't work as the circle perimeter is linked proportionally to the x value making a rectangle a better solution

For the improvements:

A circular venue would provide the maximum area.

If I thought in 3D terms, would a tiered seating plan increase the area?

Is there anything else you think I should add?

Thanks

## What is optimisation and best use of space?

Optimisation and best use of space is the process of maximizing the efficiency and functionality of a given space. It involves finding the most effective layout and design for a space to meet its intended purpose.

## Why is optimisation and best use of space important?

Optimisation and best use of space is important because it allows for the most efficient use of resources, whether it be in a home, office, or public space. It also helps to increase productivity, improve functionality, and create a more visually appealing environment.

## What factors should be considered when optimizing a space?

When optimizing a space, factors such as the intended purpose of the space, the available resources, the target audience, and any specific requirements or limitations should be taken into consideration. Other factors may include safety, accessibility, and aesthetics.

## What are some common techniques for optimizing a space?

Some common techniques for optimizing a space include proper space planning, efficient storage solutions, smart furniture placement, utilization of natural light, and the use of multipurpose furniture and accessories. Other techniques may include color and texture coordination, decluttering, and incorporating technology.

## How can technology be used to optimize a space?

Technology can be used to optimize a space in various ways, such as through the use of smart home systems, energy-efficient appliances, and automated lighting and temperature controls. Virtual and augmented reality can also be utilized for space planning and visualization, while apps and software can assist with organization and task management.

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