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An economy is based on three sectors, agriculture, manufacturing, and energy. Production of a dollar's worth of agriculture requires inputs of $0.30 from agriculture, $0.30 from manufacturing, and $0.30 from energy. Production of a dollar's worth of manufacturing requires inputs of $0.30 from agriculture, $0.30 from manufacturing, and $0.30 from energy. Production of a dollar's worth of energy requires inputs of $0.30 from agriculture, $0.40 from manufacturing, and $0.30 from energy. Find the output for each sector that is needed to satisfy a final demand of $10 billion for agriculture, $79 billion for manufacturing, and $80 billion for energy.

An economy is based on three sectors, agriculture, manufacturing, and energy. Production of a dollar's worth of agriculture requires inputs of $0.30 from agriculture, $0.30 from manufacturing, and $0.30 from energy. Production of a dollar's worth of manufacturing requires inputs of $0.30 from agriculture, $0.30 from manufacturing, and $0.30 from energy. Production of a dollar's worth of energy requires inputs of $0.30 from agriculture, $0.40 from manufacturing, and $0.30 from energy. Find the output for each sector that is needed to satisfy a final demand of $10 billion for agriculture, $79 billion for manufacturing, and $80 billion for energy.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.4: Matrix Inverses
Problem 60E
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An economy is based on three sectors, agriculture, manufacturing, and energy. Production of a dollar's worth of agriculture requires inputs of $0.30 from agriculture, $0.30 from manufacturing, and $0.30 from energy. Production of a dollar's worth of manufacturing requires inputs of $0.30 from agriculture, $0.30 from manufacturing, and $0.30 from energy. Production of a dollar's worth of energy requires inputs of $0.30 from agriculture, $0.40 from manufacturing, and $0.30 from energy. Find the output for each sector that is needed to satisfy a final demand of $10 billion for agriculture, $79 billion for manufacturing, and $80 billion for energy.
Transcribed Image Text:An economy is based on three sectors, agriculture, manufacturing, and energy. Production of a dollar's worth of agriculture requires inputs of $0.30 from agriculture, $0.30 from manufacturing, and $0.30 from energy. Production of a dollar's worth of manufacturing requires inputs of $0.30 from agriculture, $0.30 from manufacturing, and $0.30 from energy. Production of a dollar's worth of energy requires inputs of $0.30 from agriculture, $0.40 from manufacturing, and $0.30 from energy. Find the output for each sector that is needed to satisfy a final demand of $10 billion for agriculture, $79 billion for manufacturing, and $80 billion for energy.
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