Assignment task: A popular college operations research book sells 5 million copies every year (both new and used) every year. Some users keep the book, and some sell back to the Q stores. Suppose that 90% of all students who buy new book sell it back, 80% of all students who buy 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. In addition, we are assuming that each book that is sold back to the store is sold to a student.
1. Please describe this situation by a Markov Chain.
2. In the steady-state (long run), how many new copies of the book will the publisher be able to sell each year?
3. Suppose that a book store's profit on each type of book is as follows,
a) New Book: $6
b) Once-used Book: $3
c) Twice-used Book: $2
d) Thrice-used Book: $1
If the steady-state census is representative of the bookstore's sales, what will be its average profit per book?
4. On average, how long a book exists in this system and how long does it take for a new book to become a thrice-used book?