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Matrix Problem: Motor Production and Component Calculation
Published on June 6, 2025
Linear-Algebra
Solve a matrix problem involving motor production and component requirements. The solution involves setting up production and component matrices and performing matrix multiplication to find the total components needed.
Question
Resolver con sus respectivos procedimientos
Answer
The problem asks us to work with matrices to represent production data and calculate required components.
First, let’s extract the given information:
Production Data:
- Model A: 100 motors of brand M1, 80 motors of brand M2 daily.
- Model B: 80 motors of brand M1, 60 motors of brand M2 daily.
- Model C: 40 motors of brand M1, 60 motors of brand M2 daily.
Component Requirements:
- For brand M1 motors: 18 screws (tornillos), 4 bushings (bujes).
- For brand M2 motors: 14 screws (tornillos), 2 bushings (bujes).
Part a) Represent the information in two matrices.
Let’s define the first matrix,
So, the production matrix
Let’s define the second matrix,
So, the component requirements matrix
Part b) Find a matrix that represents the daily quantity of screws and bushings needed for the assembly of each of the three motor models.
To find the total daily quantity of screws and bushings needed for each model, we need to multiply the production matrix
Let
The dimensions of
The dimensions of
The resulting matrix
The dimensions of
The resulting matrix
Let’s perform the matrix multiplication:
For the first row (Model A):
- Screws:
- Bushings:
For the second row (Model B):
- Screws:
- Bushings:
For the third row (Model C):
- Screws:
- Bushings:
So, the resulting matrix
This matrix
The final answer is