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,

, to represent the daily production of each model for each brand. The rows will represent the models (A, B, C) and the columns will represent the brands (M1, M2).

So, the production matrix

is:

Let’s define the second matrix,

, to represent the component requirements for each brand. The rows will represent the brands (M1, M2) and the columns will represent the components (screws, bushings).

So, the component requirements matrix

is:

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

by the component requirements matrix

. The resulting matrix will have rows representing the models (A, B, C) and columns representing the components (screws, bushings).

Let

be the resulting matrix.

The dimensions of

are

.
The dimensions of

are

.
The resulting matrix

will have dimensions

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

is:

This matrix

represents the daily quantity of screws and bushings needed for the assembly of each of the three motor models. The rows correspond to Models A, B, and C, respectively, and the columns correspond to screws and bushings, respectively.

The final answer is

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features

Matrix Problem: Motor Production and Component Calculation

Question

Answer

Related math solutions

Unlock the Web Version Forever

Related math solutions