Question

A is an input-output matrix of an industry and D is the demand matrix. find the amount of each product that must be produced in order to meet the demand. give your answer in correct matrix form. A= [0, 0.2, 0.25; 0.2, 0, 0.25; 0.2, 0, 0], D= [1800; 8100; 2700]

Answer 1

Answer: The amount of each product would be

`AD=\left[\begin{array}{ccc}2295\\1035\\360\end{array}\right]`

Explanation:

Since we have given that

`A=\left[\begin{array}{ccc}0&0.2&0.25\\0.2&0&0.25\\0.2&0&0\end{array}\right]\\\\and\\\\D=\left[\begin{array}{ccc}1800\\8100\\2700\end{array}\right]`

Here, A is an input output matrix and D is the demand matrix.

We need to find the amount of each product in order to meet the demand.

So, the Product of AD is the amount of each product.

So, it becomes,

`AD=\left[\begin{array}{ccc}0&0.2&0.25\\0.2&0&0.25\\0.2&0&0\end{array}\right]\left[\begin{array}{ccc}1800\\8100\\2700\end{array}\right]\\\\AD=\left[\begin{array}{ccc}0* 1800+0.2* 8100+0.25* 2700\\0.2* 1800+0* 8100+0.25* 2700\\0.2* 1800+0* 8100+0* 2700\end{array}\right] \\\\AD=\left[\begin{array}{ccc}2295\\1035\\360\end{array}\right]`

So, the amount of each product would be

`AD=\left[\begin{array}{ccc}2295\\1035\\360\end{array}\right]`