A closed model for an economy identifies government, the profit sector, the nonprofit sector, and households as its industries. Each unit of government output requires 0.4 unit of government input, 0.3 unit of profit sector input, 0.3 unit of nonprofit sector input, and 0.4 unit of households input. Each unit of profit sector output requires 0.3 unit of government input, 0.4 unit of profit sector input, 0.2 unit of nonprofit sector input, and 0.5 unit of households input. Each unit of nonprofit sector output requires 0.2 unit of government input, 0.2 unit of profit sector input, 0.2 unit of nonprofit sector input, and 0.7 unit of households input. Each unit of households output requires 0.05 unit of government input, 0.2 unit of profit sector input, 0.2 unit of nonprofit sector input, and 0.25 unit of households input.
Write the augmented matrix for this closed model of the economy according to the Closed Leontief model as described in Mathematical Applications for the Management, Life, and Social Sciences By Ronald J. Harshbarger, James J. Reynolds.