Find the production schedule for the technology matrix and demand vector given below: 0.4 0.1 5 A = 0.4 0.6 0.8 D 8 0.1 0.3 0.2 3 X =
Find the production schedule for the technology matrix and demand vector given below: 0.4 0.1 5 A = 0.4 0.6 0.8 D 8 0.1 0.3 0.2 3 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
![**Problem Statement:**
Find the production schedule for the technology matrix and demand vector given below:
\[
A = \begin{bmatrix}
0.4 & 0.1 & 0 \\
0.4 & 0.6 & 0.8 \\
0.1 & 0.3 & 0.2
\end{bmatrix}, \quad
D = \begin{bmatrix}
5 \\
8 \\
3
\end{bmatrix}
\]
\[
X = \begin{bmatrix}
□ \\
□ \\
□
\end{bmatrix}
\]
**Explanation:**
- The matrix \( A \) is the technology matrix that represents the input-output coefficients for a production model. It is a 3x3 matrix where each element describes the proportion of resources from one sector needed to produce a unit of output in another sector.
- The vector \( D \) is the demand vector, which indicates the external demand for products from each sector. It is a 3x1 matrix.
- The vector \( X \) represents the production schedule needed to meet the external demand and internal technological requirements. It is the solution to the equation \( X = (I - A)^{-1} D \), where \( I \) is the identity matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73f3aba6-2965-4a12-ac09-7f2036eb7204%2F2cf7fd56-f2d0-4154-9025-c8cc5c57a5bc%2Fyjdxgrn_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the production schedule for the technology matrix and demand vector given below:
\[
A = \begin{bmatrix}
0.4 & 0.1 & 0 \\
0.4 & 0.6 & 0.8 \\
0.1 & 0.3 & 0.2
\end{bmatrix}, \quad
D = \begin{bmatrix}
5 \\
8 \\
3
\end{bmatrix}
\]
\[
X = \begin{bmatrix}
□ \\
□ \\
□
\end{bmatrix}
\]
**Explanation:**
- The matrix \( A \) is the technology matrix that represents the input-output coefficients for a production model. It is a 3x3 matrix where each element describes the proportion of resources from one sector needed to produce a unit of output in another sector.
- The vector \( D \) is the demand vector, which indicates the external demand for products from each sector. It is a 3x1 matrix.
- The vector \( X \) represents the production schedule needed to meet the external demand and internal technological requirements. It is the solution to the equation \( X = (I - A)^{-1} D \), where \( I \) is the identity matrix.
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