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]
Accepted Solution
A:
Answer: The amount of each product would be[tex]AD=\left[\begin{array}{ccc}2295\\1035\\360\end{array}\right][/tex]Step-by-step explanation:Since we have given that [tex]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][/tex]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,[tex]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\times 1800+0.2\times 8100+0.25\times 2700\\0.2\times 1800+0\times 8100+0.25\times 2700\\0.2\times 1800+0\times 8100+0\times 2700\end{array}\right] \\\\AD=\left[\begin{array}{ccc}2295\\1035\\360\end{array}\right][/tex]So, the amount of each product would be[tex]AD=\left[\begin{array}{ccc}2295\\1035\\360\end{array}\right][/tex]