The USC Bookstore is preparing for the upcoming semester and needs to stock textbooks for Operations Management. The cost to acquire each textbook from the publisher is $$75$ and can be sold to students for $$100.$ Any excess books are used as rentals for several years and have a lifetime value of $$20.$ If a student requests an Ops textbook and the bookstore is out of stock, they offer the student a $$25$ Amazon Gift Card so they can purchase it online through Amazon. Based on data from past semesters, the bookstore estimates there is a $5\%$ chance they will sell $600$ textbooks, a $10\%$ chance they will sell $500,$ a $45\%$ chance they will sell $400$ and a $40\%$ chance they will sell $300.$ You can assume they will sell exactly $600,500,400,$ or $300$ textbooks. a$)(2$ points$)$ What is the expected demand for Ops books?