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Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs. The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $88,200 for sales and $29,400 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole number)

Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs. The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $88,200 for sales and $29,400 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole number)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs. The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $88,200 for sales and $29,400 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole numher)
Transcribed Image Text:Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs. The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $88,200 for sales and $29,400 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole numher)
Suppose that the economy of a small nation has an electronics industry, a steel industry, and an auto industry, with the following technology matrix. E SA 0.6 0.2 0.2 Electronics A = 0.1 0.4 0.5 Steel 0.1 0.2 0.2 Autos If the nation wishes to have surpluses of 120 units of electronics production, 223 units of steel production, and 235 automobiles, find the gross production of each industry.
Transcribed Image Text:Suppose that the economy of a small nation has an electronics industry, a steel industry, and an auto industry, with the following technology matrix. E SA 0.6 0.2 0.2 Electronics A = 0.1 0.4 0.5 Steel 0.1 0.2 0.2 Autos If the nation wishes to have surpluses of 120 units of electronics production, 223 units of steel production, and 235 automobiles, find the gross production of each industry.
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