QUESTION 5 Dan's Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails at $28.00. The publisher sells the book to Dan at $22.00. Dan will dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Dan estimates that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250. Suppose Dan orders 1500 copies. What is Dan's expected profit? Report your answer to two decimal places.QUESTION 1 Quick Print Inc. uses plan paper for copying needs. Weekly demand for that paper follows a normal distribution with mean 100 and standard deviation 50 (measured in reams). Each week, a replenishment order is placed with its supplier and the order arrives one week later. All copying orders that cannot be satisfied immediately due to the lack of paper are backordered. Suppose it wants to have an in-stock probability of at least 0.998. What order-up-to level should it use? Report your answer to the nearest integer.QUESTION 3 BASF sells customized petrochemical catalysts that are produced in a plant in Germany. Many of their customers are in North America and transportation is done via ocean carrier. They can purchase container capacity in advance at the price of $3500 per container. However, if they advance purchase containers, they bear the risk of not knowing their exact needs for containers. In particular, here is a forecast of their needs for June (i.e., a density and distribution function): f(q) F(Q) Q f(q) 0.1810 0.0952 11 1.0201 (.8997 0.1482 0.2592 12 0.0164 1.9179 0.1213 0.3935 13 4.0134 1.0993 0.5034 14 0.0110 0.0813 0.5934 15 a.oo90 5 0.0666 0.6671 16 6 0.0545 0.7275 17 B. 6060 0.0446 0.7769 18 1.0049 0.1365 0.8173 19 LOD48 0.0299 0.8504 20 0.0033 10 0.0245 0.8775 If they purchase a container in advance and don't actually need it, then they will fill it with some excess "filler" product and store it in North America until it can be sold. The expected extra storage cost is $325 per container. For example, if their needs are for 2 containers but they advanced purchased 3 containers, then they ship all three containers and incur an extra $325 charge for the 1 container filled with "filler" product. Containers purchased on the spot market (after they learn their needs) are expected to cost $4500 per container. For example, they may advance purchase 1 container but discover that they need 3 containers, in which case they would purchase an additional 2 containers at $4500 each. How many containers should they advance purchase to minimize their costs? Report your answer as an integer