Basic Logic of "Formulating"

[Severo]

The purpose of this thread is to explain the basic logic of how a formula comes to be, and to explain where do Constantes come from. Please forgive my English

Simple to understand, the steps are in order

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Part [math]\alpha[/math]:

Let us take a simple problem

 

"In a factory, 2 workers working 6 hours, 5 days a week, produce 100."

 

Now let us think, the more workers we have the more blocks we produce

so the number of workers is directly proportianal to the number of blocks produced.

 

Also, the more hours they work, the more blocks they will produce. So the number of hours is also directly proportional to the number of blocks produced.

 

Also(again), the more days they work the more blocks they will produce. So the number of days is also directly proportional to the number of blocks produced.

 

Let us assign variables to each factor

 

B = Number of Block

H = Number of hours per day

W = Number of Workers

D = Days they work in a week

 

We conclude that

([math]\alpha[/math] is the simbol of proportionality)

 

B [math]\alpha[/math] H

B [math]\alpha[/math] W

B [math]\alpha[/math] D

______________________

 

B [math]\alpha[/math] H.W.D

 

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Part [math]\beta[/math]:

 

To transform a proportionality into an equality we must multiply one of the sides by a constant

 

B [math]\alpha[/math] H.W.D

 

we will multiply one of the sides by [math]\varphi[/math]

 

B = [math]\varphi[/math](H.W.D)

 

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Part [math]\chi[/math]:

 

Now we must calculate the constante.

 

B = [math]\varphi[/math](H.W.D)

 

using the information in Parte [math]\alpha[/math]

 

100 = [math]\varphi[/math](6.2.5)

100 = [math]\varphi[/math].60

100/60 = [math]\varphi[/math]

[math]\varphi[/math] = 5/3 = 1,66...

 

we have found the value of the variable, now we can calculte any problem involving this information.

 

Example

 

In the same factory as the last problem, we have 5 workers, working 3 hours a day, 2 days a week. How many blocks will they produce?

 

B = [math]\varphi[/math](H.W.D)

B = (5/3) . (3.5.2)

B = (5/3) . 30

B = 5.30/3

B = 50 Blocks

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I made this up by myself, but many other people probably have thought of this already.

Isn't math beutiful =D

[alan2here]

(2 * 6 * 5) / 100 = 0.6 blocks per worker per hour.

 

This really is not enough. I can see why you may be annoyed. You should tell your workers to work more quickly or get another job.

[the tree]

First up, the 'is proportional to' symbol can be used in LaTeX by typing \propto, use this over alpha to avoid confusion.

 

But really linear equations aren't a great model for this type of thing since workers and units produced are always going to come into integers and there'll always be plenty of other limitations in place. In short, none of this is really directly proportional.

 

You may well be interested in critical path analysis which is an incredibly powerful tool for modelling and optimising this type of situation.