Problem 2 (Leontifs Aggregated Industries for the 1958 US economy). The economist Leontief used US data from 1958 to treat most of the US economy in terms of eight aggregated industries, which we will call Food (includes food and drugs), Housewares (includes textiles, clothing, and furnishings), Machinery, Transportation (Leontief includes transportation equipment and consumer appliances here), Construction, Metals, Energy, and Chemicals. Leontiefs research indicates that, in producing $1 worth of output from the Food industry, $0.1993, $0.0045, $0.0056, $0.0048, $0.0152, $0.0135, $0.0283, $0.0256 worth of input is required from the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. Similarly, in producing $1 worth of output from the Housewares industry, $0.0150, $0.3511, $0.0059, $0.0043, $0.0060, $0.0130, $0.0179, $0.0282 worth of input is required from the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. In producing $1 worth of output from the Machinery industry, $0.0076, $0.0043, $0.1093, $0.0384, $0.0054, $0.1447, $0.0175, $0.0095 worth of input is required from the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. In producing $1 worth of output from the Transportation industry, $0.0065, $0.0152, $0.0382, $0.2187, $0.0057, $0.1120, $0.0149, $0.0088 worth of input is required from the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. In producing $1 worth of output from the Construction industry, $0.0075, $0.0111, $0.0203, $0.0199, $0.0007, $0.0939, $0.0403, $0.0177 worth of input is required from the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. In producing $1 worth of output from the Metals industry, $0.0059, $0.0061, $0.0291, $0.0172, $0.0101, $0.2827, $0.0605, $0.0163 worth of input is required from the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. In producing $1 worth of output from the Energy industry, $0.0054, $0.0016, $0.0101, $0.0045, $0.0382, $0.0096, $0.1708, $0.0177 worth of input is required from the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. In producing $1 worth of output from the Chemicals industry, $0.0328, $0.0052, $0.0170, $0.0045, $0.0059, $0.0407, $0.0958, $0.2124 worth of input is required from the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. (a) Write the input-output matrix for most of the US economy in 1958, as represented by the above eight aggregated industries. (b) Leontief indicates that the dollar values of the outputs from the aggregated industries to be supplied to outside consumers in 1958 were $58,728 million, $21,369 million, $13,385 million, $38,691 million, $65,117 million, $2,244 million, $23,851 million, and $3,218 million for the Food, Housewares, Machinery, Transportation, Construction, Metals, Energy, and Chemicals industries, respectively. What were the proper production amounts for each of these eight sectors of the US economy in 1958? Clearly label your answers with the industry names and the dollar amounts, rounding to the nearest unit (our unit of measurement for production amounts is $1 million).