Two car rental companies A and B are competing for customers at certain airports. A study has been made of customer satisfaction with the various companies. The results are expressed by the following matrix R. The first column of R implies that 75% of those currently using rental company A are satisfied and intend to use A next time, while 25% of those using A are dissatisfied and plan to use B next time. There is a similar interpretation to the second column ofR. (from) (to) A B R = [75% 20%] A 25% 80% B Modify the matrix R to obtain a transition matrix P for a Markov chain that describes the rental patterns. If the current trends continue, how will the rental distribution eventually settle? Express the distribution in percentages that use companies A and B.

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