My second discussion topic for my Math for Modelers class was to present a system of equations that I could or would come across professionally.
Since I'm currently working at an apparel company, I thought the following would be the perfect fit.
To make it simple, let's imagine the following. There are a lot more players in the game but for now, let's say in one specific part of the business we have two following functions:
The Designers are exactly what the titles deem them. They are the ones conceptualizing the concept of our apparel, bringing them to life from their inspiration and onto paper. The Sample Sewers take their vision and bring it to life with real fabric and material.
Assumptions:
We are focusing on tees and denim for our fall line. On average, it usually takes the designers 10 hours to conceptualize the design of the tees. It takes the Sample Sewers 20 hours to create the tees. For denim, it usually takes the designers 40 hours to conceptualize the design and 60 hours for the Sample Sewers to create them.
My question: how much would we be able to create if the Designers had 1000 hours and the Sample Sewers only had 500 hours to devote to this project for the fall line?
Solution to come in both Echelon and Gauss-Jordan methods!
Since I'm currently working at an apparel company, I thought the following would be the perfect fit.
To make it simple, let's imagine the following. There are a lot more players in the game but for now, let's say in one specific part of the business we have two following functions:
- Designers
- Sample Sewers
The Designers are exactly what the titles deem them. They are the ones conceptualizing the concept of our apparel, bringing them to life from their inspiration and onto paper. The Sample Sewers take their vision and bring it to life with real fabric and material.
Assumptions:
We are focusing on tees and denim for our fall line. On average, it usually takes the designers 10 hours to conceptualize the design of the tees. It takes the Sample Sewers 20 hours to create the tees. For denim, it usually takes the designers 40 hours to conceptualize the design and 60 hours for the Sample Sewers to create them.
My question: how much would we be able to create if the Designers had 1000 hours and the Sample Sewers only had 500 hours to devote to this project for the fall line?
Solution to come in both Echelon and Gauss-Jordan methods!
update
System of equations:
10x + 40y = 1,000
20x + 60y = 500
However, after working the problem out and collaborating with classmates on this, the results are actually faulty.
The numbers in my problem do not work in real life. I was definitely bummed out. See, when we solve it, x = -200, which means that we would be making negative clothes. I don't think that's possible.
But there will soon be a solution! Soon to come in my course, we'll learn how to change the language of our equations to make these two lines maximums so that x and y can be positive integers.
On a side note, as we dive into python, which has been incredibly intimidating to learn, the math becomes so simple. Thanks to one of my classmates that shared her code to solve her system of equations, I was able to tweak it to solve mine.
Here's the python code:
10x + 40y = 1,000
20x + 60y = 500
However, after working the problem out and collaborating with classmates on this, the results are actually faulty.
The numbers in my problem do not work in real life. I was definitely bummed out. See, when we solve it, x = -200, which means that we would be making negative clothes. I don't think that's possible.
But there will soon be a solution! Soon to come in my course, we'll learn how to change the language of our equations to make these two lines maximums so that x and y can be positive integers.
On a side note, as we dive into python, which has been incredibly intimidating to learn, the math becomes so simple. Thanks to one of my classmates that shared her code to solve her system of equations, I was able to tweak it to solve mine.
Here's the python code:
import numpy
from numpy import *
from numpy.linalg import *
#Problem
#M: 10x+40y=1000
#F: 20x + 60y = 500
A= [[10,40],[20,60]]
A= matrix(A)
print ('\nMatrix A')
print A
B= [[1000],[500]]
B= matrix(B)
print ('\nMatrix B')
print B
IA= inv(A)
print ('\nInverse of A')
print IA
C= dot(IA,B)
print ('\nSolution')
print C
The solution from python:
Matrix A
[[10 40]
[20 60]]
Matrix B
[[1000]
[ 500]]
Inverse of A
[[-0.3 0.2 ]
[ 0.1 -0.05]]
Solution
[[-200.]
[ 75.]]
It was a nice try, right? I hope I don't lose points on this assignment since my supposed real life system of equations didn't work out :)