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.