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Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 2.6 - Problem 2e
Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 2.6 - Problem 2e

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# Answer: Exercises refer to an economy that is divided into

ISBN: 9780321982384 49

## Solution for problem 2E Chapter 2.6

Linear Algebra and Its Applications | 5th Edition

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Problem 2E

Exercises refer to an economy that is divided into three sectors-manufacturing, agriculture, and services. For each unit of output, manufacturing requires .10 unit from other companies in that sector, .30 unit from agriculture, and .30 unit from services. For each unit of output, agriculture uses .20 unit of its own output, .60 unit from manufacturing, and .10 unit from services. For each unit of output, the services sector consumes. 10 unit from services, .60 unit from manufacturing, but no agricultural products. Determine the production levels needed to satisfy a final demand of 18 units for agriculture, with no final demand for the other sectors. (Do not compute an inverse matrix.)

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Solution:-Step1Given thatAn economy that is divided into three sectors-manufacturing, agriculture, and services. For each unit of output, manufacturing requires .10 unit from other companies in that sector, .30 unit from agriculture, and .30 unit from services. For each unit of output, agriculture uses .20 unit of its own output, .60 unit from manufacturing, and .10 unit from services. For each unit of output, the services sector consumes. 10 unit from services, .60 unit from manufacturing, but no agricultural products.Step2To findDetermine the production levels needed to satisfy a final demand of 18 units for agriculture, with no final demand for the other sectors. (Do not compute an inverse matrix.)Step3First column :- unit consumption vector for manufacturing.Second column :- unit consumption vector for agriculture.Third column:- unit consumption vector for services.Consumption matrixC= Let x= Equation for demandx=Cx+dSo, d=x-Cxd= = = System of equation has the augmented matrix Hence x=(33.33, 35.00, 15.00)Therefore, the production levels needed to satisfy a final demand of 18 units for agriculture, with no final demand for the other sectors is (33.33, 35.00, 15.00).

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