Given an exchange table for the economy that consists of three sectors. Distribution of Output from: Transportation Manufacturing Services Purchased by: 0.3 0.8 Transportation 0.5 0.1 0.1 Manufacturing 0.5 0.6 0.1 Services Denote the total annual output (in dollars) of the transportation, manufacturing and services sectors by p,, PM and ps, respectively. (a) Formulate a homogeneous system of linear equations to describe the income/expenses requirements for the sectors. (b) Write (a) as a single matrix equation. (c) Solve (a) by applying Gauss-Jordan elimination method. (d) Using the result obtained in (c), what is the set of equilibrium prices for the sectors when the service sector has an annual output of $80?
Given an exchange table for the economy that consists of three sectors. Distribution of Output from: Transportation Manufacturing Services Purchased by: 0.3 0.8 Transportation 0.5 0.1 0.1 Manufacturing 0.5 0.6 0.1 Services Denote the total annual output (in dollars) of the transportation, manufacturing and services sectors by p,, PM and ps, respectively. (a) Formulate a homogeneous system of linear equations to describe the income/expenses requirements for the sectors. (b) Write (a) as a single matrix equation. (c) Solve (a) by applying Gauss-Jordan elimination method. (d) Using the result obtained in (c), what is the set of equilibrium prices for the sectors when the service sector has an annual output of $80?
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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Transcribed Image Text:Given an exchange table for the economy that consists of three sectors.
Distribution of Output from:
Transportation
Manufacturing
Services
Purchased by:
0.3
0.8
Transportation
0.5
0.1
0.1
Manufacturing
0.5
0.6
0.1
Services
Denote the total annual output (in dollars) of the transportation, manufacturing and services
sectors by p,, PM and ps, respectively.
(a) Formulate a homogeneous system of linear equations to describe the income/expenses
requirements for the sectors.
(b) Write (a) as a single matrix equation.
(c) Solve (a) by applying Gauss-Jordan elimination method.
(d) Using the result obtained in (c), what is the set of equilibrium prices for the sectors when
the service sector has an annual output of $80?
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