2. The USC Student Store is preparing for May commencement and needs to stock graduation packages (cap, gown, and tassel sets). The cost to acquire each set is $75 from the supplier and can be sold to graduating students for $100. Any excess sets must be stored until next year's graduation, depreciating to a value of $20 due to storage costs and style changes. If a student can't get their regalia from the student store, they must rush-order directly from the supplier at a higher cost, damaging the store's reputation with students and families and creating an estimated negative impact of $25 per stockout. Based on data from past graduations, the store estimates there is a 5% chance they will sell 600 sets, 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 sets. a) (2 points) What is the expected demand for graduation sets? b) (4 points) The manager of the student store (who hasn't taken BUAD 311) is adamant about ensuring that every student can get their regalia in time for graduation photos and ceremonies, so wants the store to be in-stock 90% of the time. How many sets should the store stock to meet this manager's requirements? c) (5 points) One of the student workers (who stocks the shelves) has taken BUAD 311 and mentions that the store is not stocking the most cost-effective quantity of graduation sets. What is the optimal order size for the USC Student Store that would maximize expected profits? d) (6 points) For this question only, ignore your previous answers and assume that the store decides to order 400 sets (this may or may not match your answer from above). With this new order size, what is the expected profit for the store, including from potential storage of excess sets or losses from stockouts?