The open Leontief model, introduced in Section 3.4, is used to model the economies of many countries throughout the world, as well as the global economy itself. The first example Leontief himself used was the American economy in 1947. He divided the economy into 42 industries (or sectors) for his original model. For purposes of this example, the data from the 42 sectors used by Leontief has been collected into just 3: agriculture, manufacturing, and services (shown in Table 1) The open sector or demand vector (which consumes only goods and services) is also present. TABLE 1 EXCHANGE OF GOODS AND SERVICES IN THE U.S. FOR 1947 (IN BILLIONS OF 1947 DOLLARS) Agriculture Manufacturing Open Sector Total Gross Output Services Agriculture 34.69 4.92 5.62 39.24 84.56 Manufacturing 5.28 61.82 22.99 60.02 163.43 10.45 25.95 42.03 130.65 219.03 Services 1. 1) For each sector, compute the surplus that consumer demand is not using