A simplified economy involves just three commodity categorie

A simplified economy involves just three commodity categories - agriculture, manufacturing, and transportation, all in appropropriate units. Production of 1 unit of agriculture requires 1/3 unit of manufacturing and 1/4 unit of transportation; production of 1 unit of manufacturing requires 1/4 unit of agriculture and 1/4 unit of transportation, and production of 1 unit of transportation requires 1/5 unit of agriculture and 1/4 unit of manufacturing. If the demand is 603 units of each commodity, how many units of each commodity should be produced? (round to the nearest whole number as neded)

Solution

The input output matrix of the problem will be given as

and the demand matrix is equal to

The matrix (I-A) will be equal to

Now we need to find the inverse of the matrix (I-A) in order to get the answer

The inverse matrix will be equal to

Now in order to find the final answer, multiply this matrix by Demand matrix, we get the final answer

The final answer is given below