Chapter 4.7, Problem 39E

Agriculture, manufacturing, energy. An economy is based on three sectors, agriculture, manufacturing, and energy. Production of a dollar's worth of agriculture requires inputs of $\$0.20$ from agriculture, $\$0.20$ from manufacturing, and $\$0.20$ from energy. Production of a dollar’s worth of manufacturing requires inputs of $\$0.40$ from agriculture $\$0.10$ from manufacturing, and $\$0.10$ from energy. Production of a dollar's worth of energy requires inputs of $\$0.30$ from agriculture, $\$0.10$ from manufacturing, and $\$0.10$ from energy. Find the output for each sector that is needed to satisfy a final demand of $\$10$ billion for agriculture. $\$15$ billion for manufacturing, and $\$20$ billion for energy.