suppose you are a manager for a book store, for each book you sell, the store makes $m, and for each book you order in advance without being sold, it costs $c fo ryou to restock them.
(1) let y be the number of books you order. Let x be the total number of books you would be able to sell. x is a random variable that follows a CDF F(x). write your profit function as functions of x and y.
(2) write out the expected profit. you may think x and y are continuous variables.
(3) derive the 1st order condition for profit maximization.
(4) find out the optimal number of books that you should order in advance.