S THE LEONTIEF INPUT–OUTPUT MODEL: An economy is divided into three sec- tors—manufacturing, agriculture, and services. For each unit of output, manufacturing requires .40 unit from other companies in that sector, .10 unit from agriculture, and .30 unit from services. For each unit of output, agriculture uses .60 unit of its own output, .30 unit from manufacturing, and .10 unit from services. For each unit of output, the services sector consumes .20 unit from services, .50 unit from manufacturing, but no agricultural products. i. Construct the consumption matrix for this economy, and determine what intermediate demands are created if agriculture plans to produce 50 units. ii. Determine the production levels needed to satisfy a final demand of 36 units for manufacturing, with no final demand for the other sectors. (Do not compute an inverse of matrix.)