28. An industrial system has two industries with the following input requirements. (a) To produce $1.00 worth of output, Industry A requires S0.30 of its own product and S0.40 of Industry B's product. (b) To produce S1.00 worth of output, Industry B requires $0.20 of its own product and $0.40 of Industry A's product. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation X = DX + E, where the external demand is -[50,000 E =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 24EQ: Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry...
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28. An industrial system has two industries with the following input
requirements.
(a) To produce $1.00 worth of output, Industry A requires
$0.30 of its own product and $0.40 of Industry B's
product.
(b) To produce $1.00 worth of output, Industry B requires
s0.20 of its own product and S0.40 of Industry A's
product.
Find D, the input-output matrix for this system. Then solve for
the output matrix X in the equation X = DX + E, where the
external demand is
50,000
30,000
Transcribed Image Text:28. An industrial system has two industries with the following input requirements. (a) To produce $1.00 worth of output, Industry A requires $0.30 of its own product and $0.40 of Industry B's product. (b) To produce $1.00 worth of output, Industry B requires s0.20 of its own product and S0.40 of Industry A's product. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation X = DX + E, where the external demand is 50,000 30,000
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