(a) Explanation Given: The input-output matrix is; [ .178 .018 .411 0 .005 0 .143 .018 .088 0 .001 0 .089 0 .035 0 .060 .003 .001 .010 .012 .063 .007 .014 .141 .252 .088 .089 .402 .124 .188 .156 .103 .255 .008 .474 ] Formula used: Calculation: Let the input output, matrix be denoted by A . Use this to obtain, ( I − A ) as follows: I − A = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] − [ .178 .018 .411 0 .005 0 .143 .018 .088 0 .001 0 .089 0 .035 0 .060 .003 .001 .010 .012 .063 .007 .014 .141 .252 .088 .089 .402 .124 .188 .156 .103 .255 .008 .474 ] This gives, ( I − A ) = [ 0.822 − 0.018 − 0.411 0 − .005 0 − 0 (b) To determine The dollar amount each sector should produce.

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 6.6, Problem 36E

(a)

To determine

To calculate: The matrix (I−A)−1 and the interpretation of the value in row two, column one of this matrix.

(b)

To determine

The dollar amount each sector should produce.

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Chapter 6.6, Problem 35E

Chapter 6.6, Problem 37E

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Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

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The matrix ( I − A ) − 1 and the interpretation of the value in row two, column one of this matrix.