7 On the average, 26 patrons per year come to the I.U.

library to borrow the I Ching (assume that interarrival times are exponential). Borrowers who find the book unavailable leave and never return. A borrower keeps a copy of the I Ching for an average of 4 weeks.

a If the library has only one copy, what is the expected number of borrowers who will come to borrow the I Ching each year and find that the book is not available?

b Suppose that each person who comes to borrow the I Ching and is unable to is considered to cost the library

$1 in goodwill. A copy of the I Ching lasts two years and costs $11. A thief has just stolen the library’s only copy. To minimize the sum of purchasing and goodwill costs over the next two years, how many copies of the I Ching should be purchased?