Please show all work Thank you An economy is based on three

Please show all work! Thank you!

An economy is based on three sectors, agriculture, manufacturing and energy. Production of a dollar s worth of agriculture requires an input of $0.10 from agriculture, $0.20 from manufacturing and $0.20 from energy. Production of a dollar\'s worth of manufacturing requires an input of $0.10 from manufacturing and $0.10 from energy. Production of a dollar\'s worth of energy requires an input of $0.30 from agriculture, $0.10 from manufacturing and $0.10 from energy. Find to the nearest tenth of a billion $s the output from each sector required to satisfy a final demand of $10 billion for agriculture, $15 billion for manufacturing and $20 billion for energy.

Solution

$10 billion agriculture = $1 billion agiculture + $2 billion manufacture + $2 billion energy

$15 billion manufacture = $1.5 billion manufacture + $1.5 billion energy

$20 billion energy = $6 billion agiculture + $2 billion manufacture + $2 billion energy

total requirement = ($1 billion agiculture + $2 billion manufacture + $2 billion energy) + ($1.5 billion manufacture + $1.5 billion energy) + ($6 billion agiculture + $2 billion manufacture + $2 billion energy)

= $7 billion agiculture + $5.5 billion manufacture + $5.5 billion energy