Re: [Phys-L] widget rate puzzle ... reasoning, scaling, et cetera

[Scott Orshan <sdorshan@aol.com>]

These type of problems contain so many unknowns that they become one of 
those mind reading problems.

Are the machines identical, and can they run simultaneously? Are they 
independent, or does the partially completed widget move from machine to 
machine in an assembly line fashion?

Can the raw material delivery rate be scaled linearly? Probably not. You 
size your loading dock, and buy sufficient forklifts to support your 
current capacity, or maybe a little more.

If you're making widgets at a higher rate, where will you put them, and 
how fast can you ship them out?

Are humans involved? Are there enough trained humans to run more machines?

Is there a reset time between widgets? I.e., does it take 4 minutes to 
make the widget, and then another minute to cycle the machinery back to 
the initial state? That would reduce the time to produce the last group 
of widgets, which could be post-processed while the machines were 
resetting for the next day.

Can the machines run continuously, or must they pause every so often to 
get oiled, have waste removed, blades changed, or be maintained in some way?

In the simplistic case of independent machines with unlimited capacity 
and no reset time, the problem stated below can be interpreted as taking 
an isolated machine 5 minutes to produce each widget. One machine would 
take 500 minutes to make 100 widgets. So you just need the original 5 
machines to produce 100 widgets in 100 minutes, or in fact, N widgets in 
N minutes, where N is a multiple of 5.

Another interesting question is how long it takes for 5 machines to make 
4 widgets, or 20 machines to make 50 widgets. What happens when you 
divide integers, and end up with a remainder? Do they still teach "modulo"?

A super excellent way to solve these classes of problems is not with 
math or physics, but by writing a program that simulates widget 
production, and allows you to vary the different parameters. It doesn't 
have to have complex graphics or controls. It just needs to print a 
timestamp every time a widget is produced.



On 1/1/2015 12:00 PM, phys-l-request@www.phys-l.org wrote:
>       It takes 5 minutes for 5 machines to make 5 widgets.
>       So, how many machines does it take to make 100
>       widgets in 100 minutes?