Find part B
  

B. What production levels are needed to meet a demand of 29 units of agriculture, 34 units of manufacturing, and 40 units of households? To find the production levels needed to satisfy the required demands, it is necessary to first find the production matrix X. Remember that X = (1 - A) D, where I is the identity matrix, A is the input-output matrix, and D is the demand matrix. Subtract the given input-output matrix A from the 3x3 identity matrix I and then find the inverse of the resulting matrix. Multiply the demand matrix D by this inverse matrix to find the production matrix X. Round the final values in the production matrix to the nearest whole number. X=(1-A)-D = 100 0 1 0 0 0 1 0.24 0.39 0.127 0.13 0.16 0.097 0.74 3.45 0.141 29 34 40 500 1772 Therefore, production levels of 500 units of agriculture, 323 units of manufacturing, and 1772 units of households are needed (approximately) to meet a demand of 29 units of agriculture, 34 units of manufacturing, and 40 units of households.