Question

An economy consists of two interdependent industries steel and lumber. It takes 0.1 unit of steel and 0.5 unit of lumber to make one unit of steel. It takes 0.2 unit of steel and 0 unit of lumber to make one unit of lumber. The economy will export 16 units of steel and 8 units of lumber next month. How many units of steel and lumber will they need to produce to meet the external demand?​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given : An economy consists of two interdependent industries steel and lumber. It takes 0.1 unit of steel and 0.5 unit of lumber to make one unit of steel. It takes 0.2 unit of steel and 0 unit of lumber to make one unit of lumber.

The economy will export 16 units of steel and 8 units of lumber next month.

To Find : How many units of steel and lumber will they need to produce to meet the external demand

Solution:

X  = AX   +  D

$A=\left[\begin{array}{ccc}0.1&0.5\\0.2&0\end{array}\right]$

$X=\left[\begin{array}{ccc}Steel\\lumbar\end{array}\right]$

$D=\left[\begin{array}{ccc}16\\ 8\end{array}\right]$

X ( I - A)  = D

=> X  = ( I - A)⁻D

$I=\left[\begin{array}{ccc}1 &0\\0&1\end{array}\right]$

$I - A=\left[\begin{array}{ccc}0.9&{-0.5}\\{-0.2}&1\end{array}\right]$

$(I - A)^{-1}= \frac{1}{8} \left[\begin{array}{ccc}10&5\\2&9\end{array}\right]$

X  = ( I - A)⁻D

$X=\left[\begin{array}{ccc}25\\13\end{array}\right]$

Hence 25  units of steel and  13 units of  lumber

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