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        riddles >> putnam exam (pure math) >> Highschool Level - Optimization - Best Fit Problem
        
(Message started by: Ledmu8 on Nov 1^st, 2012, 4:59pm)

Title: Highschool Level - Optimization - Best Fit Problem
Post by Ledmu8 on Nov 1^st, 2012, 4:59pm

Hello all! My name is Lucas and I am a highschool Student. I was searching around the Internet for problems with solutions for questions similar to those of my assignment, and I stumbled across this website.

Whilst it may not hold the answer for my problems straight away, there are so many different answers to this problem and I’ll have to re-write this into my own words and with my own equations at the end anyway (because taking your answer would be plagiarism now wouldn’t it?), so I’m just here for ideas and ways to reach any particular solution.

The parameters of the problem are as follows:

The maximum amount of two different sized large discs need to be cut out of two (2) sheets of metal 5m x 4m
Each of the discs must have a circle cut out of the middle
The larger of the two discs outer edge may be anywhere between 60cm and 65cm in diameter
The inside of that very same disc may be anywhere between 40 and 41cm in diameter
The smaller of the two discs outside edge may be anywhere between 42 and 45cm in diameter (so never can the smaller disc fit inside the larger)
The inside of that disc may be anywhere between 34 and 35cm in diameter
The proportion of smaller discs to large discs is 2:3 to 3:2, so any ratio in between

A few things need to be kept in mind if you are figuring out this problem:

1. There must be as little waste as possible. So the size of the insides to me looks like it servers no other purpose other than to make the question look more complex than it is, so I recommend you go with the smaller value (unless someone can come up with a reason otherwise?)

2. You have two sheets to work with, so there can be any combination of large discs and small discs on either sheet (even large ones on one sheet and small ones on the other), as long as the total discs in the end are equal to the ratio of 2:3 to 3:2

3. The equation to figure out a point (x or y value on the edge of a circle) on a circle (on a Cartesian plane) is the equation of (x_edge - x_{origin of circle})² + (y_edge - y_{origin of circle})²= radius²

If you need more clarification or anything just let me know, I’ll be figuring out this problem at the same time as any of you guys might so if I beat you to the punch I’ll put my solution up as well. However because of the scale of the problem this will take quite some time, so it’s a problem that can be done and re-done time and time again.

Good luck and have fun!
:D

P.S: A little side problem, it seems every time I do a single action (for example changing from one topic to the other) and then do an action required for me to be logged it, it logs me off. It is quite frustrating to say the least.

Title: Re: Highschool Level - Optimization - Best Fit Pro
Post by towr on Nov 2^nd, 2012, 12:04am

This doesn't seem like problem where you can easily prove an optimal answer; rather it seems more like a contest of who can get the best result with trial and error (or a computer program).
I'll try and err some this afternoon and see how far I get.

on 11/01/12 at 16:59:13, Ledmu8 wrote:

P.S: A little side problem, it seems every time I do a single action (for example changing from one topic to the other) and then do an action required for me to be logged it, it logs me off. It is quite frustrating to say the least.

It has been reported a couple times before, but we've never been able to find out what causes it. It could be caching, or your IP changing, or something else entirely. Do you have the same problem on other browsers?

Title: Re: Highschool Level - Optimization - Best Fit Pro
Post by Grimbal on Nov 2^nd, 2012, 7:56am

Just to clarify:

What must be optimized, the amount of material used (i.e. minimize wastage) or the number of discs produced.

Title: Re: Highschool Level - Optimization - Best Fit Pro
Post by Ledmu8 on Nov 4^th, 2012, 4:22pm

I do apologise for the late response, I had a busy weekend.

What must be optimised is both the number of discs that can be created as well as the amount of material used.

I agree Towr, there are just too many variables for it to have a clear cut answer. I'll post my progress soon... ish...

Currently I am using Google Chrome, I'll try with Internet Explorer and Firefox.