Suppose that the economy of a small nation has an electronics industry, a steel industry, and an auto industry, with the following technology matrix. S A 0.6 0.2 0.2 Electronics A = 0.1 0.4 0.5 Steel 0.1 0.2 0.2 Autos If the nation wishes to have surpluses of 102 units of electronics production, 244 units of steel production, and 247 automobiles, find the gross production of each industry. electronics units steel units autos units

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 68E
icon
Related questions
Question
Suppose that the economy of a small nation has an electronics industry, a steel industry, and an auto industry, with the following technology matrix.
E
S A
0.6 0.2 0.2
Electronics
A =
0.1 0.4 0.5
Steel
0.1
0.2 0.2
Autos
If the nation wishes to have surpluses of 102 units of electronics production, 244 units of steel production, and 247 automobiles, find the gross production of each industry.
electronics
units
steel
units
autos
units
Transcribed Image Text:Suppose that the economy of a small nation has an electronics industry, a steel industry, and an auto industry, with the following technology matrix. E S A 0.6 0.2 0.2 Electronics A = 0.1 0.4 0.5 Steel 0.1 0.2 0.2 Autos If the nation wishes to have surpluses of 102 units of electronics production, 244 units of steel production, and 247 automobiles, find the gross production of each industry. electronics units steel units autos units
Expert Solution
Step 1

Suppose they the economy of a small nation has an electronics industry, a steel industry and an auto industry.

Let 

    x units is the gross production of electronics industry.

    y units is the gross production of steel industry.

    z units is the gross production of auto industry.

The production vector is  

        P = (x  y  z)t

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Markov Processes and Markov chain
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning