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An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.20 worth of electricity, and $0.20 worth of steel; the electric industry needs $0.02 worth of coal, $0.04 worth of electricity, and $0.03 worth of steel; and the steel industry needs $0.30 worth of coal and $0.02 worth of steel. The sales demand is estimated to be $1 billion for coal, $3 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand? Set up the input-output matrix. Coal Electric Steel Coal 0.01 0.02 0.30 Electric Steel 0.20 0.04 0 0.20 0.03 0.02 The coal industry should produce $☐ billion the electric industry should produce $ ☐ billion, and the steel industry should produce $ ☐ billion. (Round the final answer to the nearest billion as needed. Round the elements of the inverse matrix to two decimal places as needed.)

An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.20 worth of electricity, and $0.20 worth of steel; the electric industry needs $0.02 worth of coal, $0.04 worth of electricity, and $0.03 worth of steel; and the steel industry needs $0.30 worth of coal and $0.02 worth of steel. The sales demand is estimated to be $1 billion for coal, $3 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand? Set up the input-output matrix. Coal Electric Steel Coal 0.01 0.02 0.30 Electric Steel 0.20 0.04 0 0.20 0.03 0.02 The coal industry should produce $☐ billion the electric industry should produce $ ☐ billion, and the steel industry should produce $ ☐ billion. (Round the final answer to the nearest billion as needed. Round the elements of the inverse matrix to two decimal places as needed.)

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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An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.20 worth of electricity, and $0.20 worth of steel; the electric industry needs $0.02 worth of coal, $0.04 worth of electricity, and $0.03 worth of steel; and the steel industry needs $0.30 worth of coal and $0.02 worth of steel. The sales demand is estimated to be $1 billion for coal, $3 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand? Set up the input-output matrix. Coal Electric Steel Coal 0.01 0.02 0.30 Electric Steel 0.20 0.04 0.20 0.03 0 0.02 The coal industry should produce $ ☐ billion the electric industry should produce $ ☐ billion, and the steel industry should produce $ (Round the final answer to the nearest billion as needed. Round the elements of the inverse matrix to two decimal places as needed.) billion.
Transcribed Image Text:An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.20 worth of electricity, and $0.20 worth of steel; the electric industry needs $0.02 worth of coal, $0.04 worth of electricity, and $0.03 worth of steel; and the steel industry needs $0.30 worth of coal and $0.02 worth of steel. The sales demand is estimated to be $1 billion for coal, $3 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand? Set up the input-output matrix. Coal Electric Steel Coal 0.01 0.02 0.30 Electric Steel 0.20 0.04 0.20 0.03 0 0.02 The coal industry should produce $ ☐ billion the electric industry should produce $ ☐ billion, and the steel industry should produce $ (Round the final answer to the nearest billion as needed. Round the elements of the inverse matrix to two decimal places as needed.) billion.
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