Explanation Given Information: The demand for business forms doubles where initial demand matrix is [ 3 1 2 ] and it is also given that Computers Semiconductors Business forms Computers Semiconductors Business forms [ .02 .02 .10 .20 .01 0 .10 .02 .01 ] = A . Formula used: The production matrix for input-output analysis is given by X = ( I − A ) − 1 D , provided the inverse of the matrix I − A exists, where A is input-output matrix, I is the identity matrix and D is a demand matrix. Calculation: Consider that initial demand matrix is, D = [ 3 1 2 ] and input-output matrix is A = [ .02 .02 .10 .20 .01 0 .10 .02 .01 ] . The 3 × 3 identity matrix is represented by I = [ 1 0 0 0 1 0 0 0 1 ] . The matrix ( I − A ) can be computed as: ( I − A ) = [ 1 0 0 0 1 0 0 0 1 ] − [ .02 .02 .10 .20 .01 0 .10 .02 .01 ] = [ 1 − .02 0 − .02 0 − .10 0 − .20 1 − .01 0 − 0 0 − .10 0 − .02 1 − .01 ] = [ .98 − .02 − .10 0 .99 0 0 − .02 .99 ] The equivalent augmented matrix for ( I − A ) is [ .98 − .02 − .10 0 .99 0 0 − .02 .99 1 0 0 0 1 0 0 0 1 ] . Compute the augmented matrix as follows: Multiply row 1 by 1 0.98 to get a leading 1 . Multiply row 1 by 0.20 and add the result to row 2 and multiply row 1 by 0.10 and add the result to row 3 . [ .98 − .02 − .10 0 .99 0 0 − .02 .99 1 0 0 0 1 0 0 0 1 ] → R 3 + ( 0.10 ) R 1 ( 1 0.98 ) R 1 R 2 + ( 0.20 ) R 1 [ 1 − .02 − .10 0 .99 − 0.02 0 − .02 .98 1.02 0 0 0.2 1 0 0.1 0 1 ] Multiply row 2 by 1 0

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 2.6, Problem 15E

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To calculate: The levels at which computer and semiconductors divisions produce if the demand for business forms doubles where initial demand matrix is [312].

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Chapter 2.6, Problem 14E

Chapter 2.6, Problem 16E

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Finite Mathematics & Its Applications (12th Edition)

Ch. 2.1 - 1. Determine whether the following systems of...Ch. 2.1 - Give the meaning of each of the following...Ch. 2.1 - 3. Perform the indicated elementary row...Ch. 2.1 - State the next elementary row operation that...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - Prob. 2E Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...

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The levels at which computer and semiconductors divisions produce if the demand for business forms doubles where initial demand matrix is [ 3 1 2 ] .

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To calculate: The levels at which computer and semiconductors divisions produce if the demand for business forms doubles where initial demand matrix is [312].

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Chapter 2 Solutions