PG2 ОPEN Turned in automatically when late peric To produce a unit of electricity, 0.12 units of electricty are required and 0.23 units of water are required. To produce a unit of water, 0.07 units of electricty are required and 0.24 units of water are required. There is an external demand for 2000 units of electricity and 4300 units of water. Let electricity be represented as sector 1 and water be represented as sector 2. Create the techonology matrix representing their relationships. 0.12 0.07 A = 0.23 0.24 Create their demand vector. 2000 D = 4300 Solve for their production vector.
PG2 ОPEN Turned in automatically when late peric To produce a unit of electricity, 0.12 units of electricty are required and 0.23 units of water are required. To produce a unit of water, 0.07 units of electricty are required and 0.24 units of water are required. There is an external demand for 2000 units of electricity and 4300 units of water. Let electricity be represented as sector 1 and water be represented as sector 2. Create the techonology matrix representing their relationships. 0.12 0.07 A = 0.23 0.24 Create their demand vector. 2000 D = 4300 Solve for their production vector.
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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![**Application: Input-Output Models PG2**
To produce a unit of electricity, 0.12 units of electricity are required and 0.23 units of water are required. To produce a unit of water, 0.07 units of electricity are required and 0.24 units of water are required. There is an external demand for 2000 units of electricity and 4300 units of water.
Let electricity be represented as sector 1 and water be represented as sector 2.
**Technology Matrix:**
Create the technology matrix \( A \) representing their relationships.
\[ A = \begin{bmatrix} 0.12 & 0.07 \\ 0.23 & 0.24 \end{bmatrix} \]
**Demand Vector:**
Create their demand vector \( D \).
\[ D = \begin{bmatrix} 2000 \\ 4300 \end{bmatrix} \]
**Production Vector:**
Solve for their production vector \( X \).
\[ X = \begin{bmatrix} \, \, \, \, \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb01ce655-4372-4af4-9606-6aca74ff4552%2Fda56c921-5bf2-4ae8-8f85-c8769ea99a11%2Flucfd3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Application: Input-Output Models PG2**
To produce a unit of electricity, 0.12 units of electricity are required and 0.23 units of water are required. To produce a unit of water, 0.07 units of electricity are required and 0.24 units of water are required. There is an external demand for 2000 units of electricity and 4300 units of water.
Let electricity be represented as sector 1 and water be represented as sector 2.
**Technology Matrix:**
Create the technology matrix \( A \) representing their relationships.
\[ A = \begin{bmatrix} 0.12 & 0.07 \\ 0.23 & 0.24 \end{bmatrix} \]
**Demand Vector:**
Create their demand vector \( D \).
\[ D = \begin{bmatrix} 2000 \\ 4300 \end{bmatrix} \]
**Production Vector:**
Solve for their production vector \( X \).
\[ X = \begin{bmatrix} \, \, \, \, \]
![### 1.6: Application: Input-Output Models PG2
#### Problem Statement
Given the input-output model, solve for the production requirements based on the following information:
**Matrix A:**
\[
A = \begin{bmatrix}
0.23 & 0.24 \\
\end{bmatrix}
\]
**Demand Vector (D):**
\[
D = \begin{bmatrix}
2000 \\
4300 \\
\end{bmatrix}
\]
#### Task
1. Create the demand vector \(D\) as provided.
2. Solve for the production vector \(X\).
**Production Vector (X) Solution:**
You must find the vector \(X\) such that the system satisfies its demands.
\[
X = \begin{bmatrix}
\ \\
\ \\
\end{bmatrix}
\]
#### Conclusion
Thus, the electricity sector should produce \( \_\_\_\_ \) units, and the water sector should produce \( \_\_\_\_ \) units. (You may round your answer to the nearest cent.)
#### Interactive Element
- **Submit Answer**: Once you’ve calculated the solution, submit your answer using the interface provided. This will be graded as part of the course assessment.
#### Notes
This exercise demonstrates the application of linear algebra in economic models, focusing on the balance of supply and demand across sectors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb01ce655-4372-4af4-9606-6aca74ff4552%2Fda56c921-5bf2-4ae8-8f85-c8769ea99a11%2F9jg4yzp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 1.6: Application: Input-Output Models PG2
#### Problem Statement
Given the input-output model, solve for the production requirements based on the following information:
**Matrix A:**
\[
A = \begin{bmatrix}
0.23 & 0.24 \\
\end{bmatrix}
\]
**Demand Vector (D):**
\[
D = \begin{bmatrix}
2000 \\
4300 \\
\end{bmatrix}
\]
#### Task
1. Create the demand vector \(D\) as provided.
2. Solve for the production vector \(X\).
**Production Vector (X) Solution:**
You must find the vector \(X\) such that the system satisfies its demands.
\[
X = \begin{bmatrix}
\ \\
\ \\
\end{bmatrix}
\]
#### Conclusion
Thus, the electricity sector should produce \( \_\_\_\_ \) units, and the water sector should produce \( \_\_\_\_ \) units. (You may round your answer to the nearest cent.)
#### Interactive Element
- **Submit Answer**: Once you’ve calculated the solution, submit your answer using the interface provided. This will be graded as part of the course assessment.
#### Notes
This exercise demonstrates the application of linear algebra in economic models, focusing on the balance of supply and demand across sectors.
Expert Solution
Step 1
Given and
We have to find the .
We have to solve
Now, we will find the .
Hence,
Now, cofactor matrix is given by
Now,
Step by step
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