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Question: please show all work please answer this i know it...

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3. APBR (The Association for Professional Basketball Research) wl hold its annual conference in Miami in 2020. Five months before the meeting, APBR must reserve rooms at the conference hotel. Currently, rooms can be reserved at a cost of $75/room. Using past data and current interest, the conference organizing committee estimates that the demand for rooms is normally distributed with μ = 450 and σ = 225. If they do not reserve enough rooms, i.e. demand exceeds supply, attendees will have to find other rooms at neighboring hotels at a cost of S80/room. The inconvenience of staying at another hotel is estimated to be S10. How many rooms should the organizing committee reserve to minimize the expected cost?

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