Suggest some optimization problems for me, please.

In summary, the conversation revolves around a group of engineering students looking for creative and challenging optimization problems or related rates that involve physics. Suggestions include finding the closest points between two curves or surfaces, determining the most profitable selling price based on supply and demand, and exploring the concept of diminishing returns in relation to education. Other ideas include using Lagrangian mechanics to turn motion into an optimization problem and creating a model of an ecosystem to find the optimal number of frogs to keep the fly population at a minimum. The conversation also mentions a mathematical optimization problem involving a function and a sphere, and how it can be applied in real life scenarios.
  • #1
SpEuler
1
0
Hi, this is my first post and most certainly not my last. I'm a young Mechanical Engineering major and I love math and physics, but on with my topic...

I'm in Calc I and we've been assigned an extra-credit group project where to do present either a related rate or an optimization problem. Everyone in my group is some sort of engineering major and we're all fairly competent with math and physics. We want to do something different that's not in our book; if we have to maximize the volume of one more box, we'll hang ourselves. I was hoping to get some suggestions for some fun, but challenging optimization problems (or related rates if you can think of very cool ones). Problems that involve physics are preferred.

Thanks.

Oh and don't take the fun out of it and post answers, but relevant formulas are welcome. =)
 
Physics news on Phys.org
  • #2
There's all sorts of things you can extremize. I can't say how hard any of them are.

Given two curves (surfaces) what two points are the closest together (farthest apart)?

Given a model of supply and demand, what is the most profitable price to sell product?

Given a model of your education's worth to the cost of school over time, at what point does staying at your university hit the point of diminishing returns?

If you're doing physics, legrangian mechanics is all about turning motion into an optimization problem, extremizing the action of a system.

Come up with a model of an eco system. How many frogs can you add to the environment in order to keep the number of flies to a minimum without critically disrupting any other wildlife?

You're a dictator of a country (CEO of a company). How much can you tax (treat) your peasants (employees) before they revolt (go on strike)?
 
  • #3
Let [itex]f(x) = 2^x - x^2[/itex].
Minimize [itex]f'(x)[/itex] over the interval [itex][4, +\infty)[/itex].
Does that tell you anything interesting?

(The optimization isn't particularly challenging, but I think the application is pretty neat)
 
  • #4
Find the biggest cone you can fit in a sphere of radius r.
 

FAQ: Suggest some optimization problems for me, please.

What is an optimization problem?

An optimization problem is a mathematical or computational problem in which the goal is to find the best possible solution from a set of possible solutions. The best solution is typically defined as the one that maximizes or minimizes a certain objective function.

Why are optimization problems important?

Optimization problems have a wide range of applications in various fields, including engineering, economics, computer science, and biology. They allow us to find the most efficient or optimal solutions to real-world problems, leading to cost savings, increased productivity, and improved decision-making.

What are some examples of optimization problems?

Some common examples of optimization problems include the shortest path problem, knapsack problem, traveling salesman problem, and linear programming problems. These problems can be solved using various techniques such as dynamic programming, greedy algorithms, and heuristics.

How are optimization problems typically solved?

Optimization problems can be solved using a variety of methods, including analytical methods, numerical methods, and metaheuristic algorithms. The choice of method depends on the problem's complexity, the available resources, and the desired level of accuracy.

Can you suggest some optimization problems for me?

Sure, here are a few optimization problems you can explore:

  • Optimizing the production process in a manufacturing plant to minimize costs
  • Finding the most efficient route for a delivery truck to make multiple stops
  • Designing a portfolio of investments to maximize returns while minimizing risk
  • Optimizing the layout of a warehouse to maximize storage space
  • Minimizing energy consumption in a building while maintaining a comfortable temperature

Similar threads

How Can I Optimize Gas Network Operations in My Master Thesis?
Replies
10
Views
2K
I Advice toward Mastering Challenging Vector Calc Problems
Replies
4
Views
1K
I Optimization problem with multiple outputs: impossible?
Replies
6
Views
2K
Optimal Size of Rocket Engine Nozzle for Vacuum Performance
Replies
26
Views
2K
Other Engineering Physics vs Pure Physics
Replies
11
Views
2K
Large Multi-variable Optimization Problem
Replies
6
Views
2K
Real life Optimization problem
Replies
9
Views
3K
Exploration in Maths: Comparing Aircraft Dimensions for Optimal Flight Profile
Replies
8
Views
7K
How to get better at optimization calculus 1 problems
Replies
2
Views
1K
Looking to start a new career in physics, need some advice
Replies
9
Views
912

Hot Threads

Recent Insights

Back
Top