Generate state matrices by recursion
A daily stock record classifies each item by its location
Use the state order warehouse and shop. Every state matrix is a column in this order. In the transition matrix, columns are current states and rows are next states
One application of the transition matrix represents one day. The initial state is S_0, before any applications, so the index counts applications
\[T = \begin{bmatrix} 0.8 & 0.4 \\ 0.2 & 0.6 \end{bmatrix}\]
The initial state column gives counts of items
\[S_0 = \begin{bmatrix} 75 \\ 125 \end{bmatrix}\]
\[S_{n+1} = T S_n\]