Question

An industrial system has two industries with the following input requirements. (a) To produce $1.00 worth of output, Industry A requires $0.20 of its own product and $0.50 of Industry B's product. (b) To produce $1.00 worth of output, Industry B requires $0.40 of its own product and $0.30 of Industry A's product. Find D, the input-output matrix for this system. A B D = A B Solve for the output matrix X in the equation X = DX + E, where E is the external demand matrix E = 10,000 20,000 . (Round to the nearest whole number.)

Answer 1

Answer:

X = 1/11 * [ 250000; 575000]

Explanation:

To find D we need to build the equation first by working out the equation further we will get the value of x then we can easily work out the equation of matrix X

X = DX + E

Let the matrix X be x,y

The equation will be

x - (0.10x + 0.20y) = 10000

y -(0.50x+0.40y) = 20000

0.9x - 0.2y = 10000

-0.5x+0.6y = 20000

The value of x is equal to 250000/11 and y is equal to 575000/11

Hence the matrix X will be

X = 1/11 * [ 250000; 575000]

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