he 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.