hello i would like u to help me with this markov chains problem thanks for ur help
The best-selling college statistics text, The Thrill of Statistics, sells 5 million copies every fall. Some users keep the book, and some sell it back to the bookstore. Suppose that 90% of all students who buy a new book sell it back, 80% of all students who buy a once-used book sell it back, and 60% of all students who buy a twice-used book sell it back. If a book has been used four or more times, the cover falls off, and it cannot be sold back.
a In the steady state, how many new copies of the book will the publisher be able to sell each year?
b Suppose that a bookstore’s proﬁt on each type of book is as follows:
New book: $6
Once-used book: $3
Twice-used book: $2
Thrice-used book: $1
If the steady-state census is representative of the bookstore’s sales, what will be its average proﬁt per book?