(Steps Shown) A town has two supermarkets, one named W and one named S. Each month 70% of the customers of W stick with W and 30% switch to S: Each month
Question: A town has two supermarkets, one named W and one named S. Each month 70% of the customers of W stick with W and 30% switch to S: Each month 80% of the customers of S stick with S and 20% switch to W: The total number of customers stays constant from month to month. Let \(w\left( n \right);s\left( n \right)\) denote the number of customers of W, S during month n. Find a matrix
\[M=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)\]so that
\[\left( \begin{matrix} w\left( n+1 \right) \\ s\left( n+1 \right) \\ \end{matrix} \right)=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)\left( \begin{matrix} w\left( n \right) \\ s\left( n \right) \\ \end{matrix} \right)\]Assume w(0) = 100; s(0) = 50. Compute, using M, the number of customers in month 1 of S, W; that is, compute w(1), s(1):
Deliverable: Word Document 
![[Steps Shown] a) For what vectors v=[la](/images/solutions/MC-solution-library-69105.jpg "[Steps Shown] a) For what vectors v=[la , b , c] does the equation")
