Reference no: EM133432388

Question: Consider a library. They carry physical and digital copies of books for borrowing. For a new bestseller, they have six digital copies and four physical copies. This question only concerns digital borrowing. Note that one digital copy can be borrowed by a single customer at a given time. Customers keep the books on average for 10 days and on average, two customers a day requests the book. 75% of the customers request a physical copies and 25% request a digital copy. If no digital copies are available for borrowing, customers join a virtual line and immediately get access to a copy once another customer returns one. You may assume that customer arrivals follow a Poisson process and service times are exponential. You may use the waiting lines spreadsheet to answer this question.

a. The library's internal performance metrics dictate the average waiting time should not exceed 3 days. Is the library meeting this performance metric? Please justify your answer by providing the relevant performance metric from the spreadsheet.

b. On average, what is the number of customers waiting to get a digital copy of the book? Please justify your answer by providing the relevant performance metric from the spreadsheet.

c. Based on the results of a recent marketing study, the cost to make a customer wait is $2.2 per day while the daily cost of having a digital copy of a book is $1.65. If the objective is to minimize total daily cost, how many digital copies of this book should the library keep?