Newspaper/Subscription/Movement of customers/Matrix/Exercise

The newspapers $A,B$ and $C$ sell subscriptions, and they compete in a local market with $100000$ customers. Within a year, one can observe the following movements.

1. The subscribers of $A$ stick with a percentage of $80\mathrm{\%}$ to $A$, $10\mathrm{\%}$ switch to $B$, $5\mathrm{\%}$ switch to $C$ and $5\mathrm{\%}$ become nonreaders.
2. The subscribers of $B$ stick with a percentage of $60\mathrm{\%}$ to $B$, $10\mathrm{\%}$ switch to $A$, $20\mathrm{\%}$ switch to $C$ and $10\mathrm{\%}$ become nonreaders.
3. The subscribers of $C$ stick with a percentage of $70\mathrm{\%}$ to $C$, nobody switches to $A$, $10\mathrm{\%}$ switch to $B$ and $20\mathrm{\%}$ become nonreaders.
4. Among the nonreaders, $10\mathrm{\%}$ subscribe to $A,B$ or $C$, the rest remains nonreaders.

a) Establish the matrix that describes the movement of customers within a year.

b) In a certain year, each of the three newspapers has $20000$ subscribers and there are $40000$ nonreaders. How does the distribution look like after a year?

c) The three newspapers expand to another city, where there are no newspapers at all so far, but also $100000$ potential customers. How many subscribers does each newspaper have (and how many nonreaders) after three years, if the same movements hold in the new city?

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