Find the production schedule for the technology matrix and demand vector given below: 0.4 1.7 3 A = 0.2 0.1 0.7 D = 0.1 0.1 0.1 X = ... ...
Find the production schedule for the technology matrix and demand vector given below: 0.4 1.7 3 A = 0.2 0.1 0.7 D = 0.1 0.1 0.1 X = ... ...
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Technology Matrix and Demand Vector Analysis**
To find the production schedule, analyze the given technology matrix \( A \) and the demand vector \( D \).
**Technology Matrix \( A \):**
\[
A = \begin{bmatrix}
0.4 & 0 & 1.7 \\
0.2 & 0.1 & 0.7 \\
0.1 & 0.1 & 0.1
\end{bmatrix}
\]
This matrix represents the technological coefficients for producing goods. Each entry \( a_{ij} \) indicates the amount of input from sector \( i \) required to produce one unit of output in sector \( j \).
**Demand Vector \( D \):**
\[
D = \begin{bmatrix}
3 \\
6 \\
5
\end{bmatrix}
\]
The vector \( D \) represents the external demand for the goods produced by each sector.
**Objective:**
Calculate the production vector \( X \) to satisfy the total demand, including internal and external requirements.
The solution involves the production vector \( X \), calculated using the formula:
\[
X = (I - A)^{-1} D
\]
Where \( I \) is the identity matrix, and \( (I - A)^{-1} \) is the inverse of the matrix \( (I - A) \). In this setup, the boxes represent placeholders for elements of \( X \), which are computed as part of finding the solution to this economic model.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36a79c17-bf73-44c3-9503-d2f30f855206%2Fea5fbee7-0a6a-4145-925f-b13ad4c76315%2Fjgfwurg_processed.png&w=3840&q=75)
Transcribed Image Text:**Technology Matrix and Demand Vector Analysis**
To find the production schedule, analyze the given technology matrix \( A \) and the demand vector \( D \).
**Technology Matrix \( A \):**
\[
A = \begin{bmatrix}
0.4 & 0 & 1.7 \\
0.2 & 0.1 & 0.7 \\
0.1 & 0.1 & 0.1
\end{bmatrix}
\]
This matrix represents the technological coefficients for producing goods. Each entry \( a_{ij} \) indicates the amount of input from sector \( i \) required to produce one unit of output in sector \( j \).
**Demand Vector \( D \):**
\[
D = \begin{bmatrix}
3 \\
6 \\
5
\end{bmatrix}
\]
The vector \( D \) represents the external demand for the goods produced by each sector.
**Objective:**
Calculate the production vector \( X \) to satisfy the total demand, including internal and external requirements.
The solution involves the production vector \( X \), calculated using the formula:
\[
X = (I - A)^{-1} D
\]
Where \( I \) is the identity matrix, and \( (I - A)^{-1} \) is the inverse of the matrix \( (I - A) \). In this setup, the boxes represent placeholders for elements of \( X \), which are computed as part of finding the solution to this economic model.
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