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The PCTM Puzzle of the Week - Solutions

The Polar Bear Ice Cream Company has a monthly revenue (a,n) after n month 
Royal Ice cream Company has a monthly revenue (b,n) after n month

(a,n)=4/5*(a,n-1) + 1/5*(b,n-1)
(b,n)=4/5*(b,n-1) + 1/5*(a,n-1)  ==>

(a,n) + (b,n)=17000$
(a,n) - (b,n)=3/5*((a,n-1)-(b,n-1))=(3/5)^2*((a,n-2)-(b,n-2))=.....=(3/5)^n*
(10000-7000)

(a,n)=1/2*(3000*(3/5)^n+17000)
(b,n)=1/2*(17000-3000*(3/5)^n) ==>

After 6 month the Polar Bear Ice Cream Company has a monthly 
revenue of (a,6)=8569.984$
 After 6 month the Royal Ice cream Company  has a monthly 
revenue of (b,6)=8430.016$

The long term distribution of income for the two companies 
will be aproximately 8500$ for each.
 

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