Suppose the coal and steel industries form a closed economy

Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $.30 of coal and $.70 of steel. Every $1 produced by steel requires $.80 of coal and $.20 of steel. Find the annual product of coal and steel if the total annual production is $20 million.

Solution

Every $1 produced by the coal industry requires $.30 of coal and $.70 of steel.

Every $1 produced by the steel industry requires $.80 of coal and $.20 of steel.

Therefore, for every $2 produced by the both the industry combinely requires $(.30 + .80) = $1.1 of coal and $(.70 + .20) = $.90 of steel.

This implies, for every $20 produced by the both the industry combinely requires $11 of coal and $9 of steel.

Hence, if the total annual production is $20 million, then it requires $11 million of coal and $9 million of steel. (Answer)