# How to Solve an Optimization Problem for Carrying a Ladder Around a Corner?

• muna580
In summary, the conversation discusses an optimization problem involving two hallways meeting at a right-angled corner. The question is to find the length of the longest ladder that can be carried horizontally around the corner. The solution involves using trigonometric functions and solving for the length of the ladder, with the given information of the widths of the hallways.
muna580
I have this optimization problem, with the solution, but I don't really understand how to do this. Can someone please explain it to me? I mean, I the solution, I got totally lost when he started working out the problem after that long paragraph. Where did he get the first equation from?

One hallway (which is 4 feet wide) meets another hallway (which is 8 feet wide) in a right-angled corner. What is the length of the longest ladder which can be carried horizontally around the corner? Give an exact answer, assuming the ladder has no width.

I don't understand what more you want. Do you see why $sin(\theta)= \frac{4}{l_1}$? Do you see why $cos(\theta)= \frac{8}{l_2}$? Do you see why $l_1+ l_2= l$?

## What is the Optimization Hallway Problem?

The Optimization Hallway Problem is a mathematical problem that involves finding the most efficient route through a hallway with obstacles. It is often used in computer science and engineering to optimize processes and algorithms.

## Why is the Optimization Hallway Problem important?

The Optimization Hallway Problem is important because it has real-world applications in various industries, such as logistics, robotics, and transportation. By finding the most efficient route through a hallway, we can save time, resources, and improve overall efficiency.

## What are the main challenges in solving the Optimization Hallway Problem?

One of the main challenges in solving the Optimization Hallway Problem is the complexity of the problem. As the number of obstacles and the length of the hallway increases, the problem becomes more difficult to solve. Additionally, finding the optimal solution may require a lot of computational power and time.

## What are some common approaches to solving the Optimization Hallway Problem?

Some common approaches to solving the Optimization Hallway Problem include brute force algorithms, heuristic algorithms, and dynamic programming. Brute force algorithms try every possible route to find the optimal solution, while heuristic algorithms use heuristics or rules of thumb to find a good solution. Dynamic programming breaks down the problem into smaller sub-problems and solves them to find the optimal solution.

## Are there any real-world examples of the Optimization Hallway Problem?

Yes, the Optimization Hallway Problem has many real-world examples, including route planning in transportation and logistics, path planning for robots, and optimizing traffic flow in cities. It is also used in computer science to optimize algorithms and data structures.

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