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Inventory Reading Mate X

Inventory Reading Mater X

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The Newsboy Model

XLRI is holding its annual convention in Dubai. Six months before the convention begins XLRI must decide how many rooms should be reserved in the convention hotel. At this time XLRI can reserve rooms at a cost of $$50$ per person, but six months before the convention XLRI doesn't know with certainty how many people will attend the convention. XL believes that the number of rooms required is normally distributed with a mean of $5000$ rooms and a standard deviation of $2000$ rooms. If the number of rooms required exceeds the number of rooms at the convention hotel, extra rooms will have to be found at neighboring hotels at at a cost of $$80$ per room. It is inconvenient for convention participants to stay at neighboring hotels. We measure this inconvenience by assessing an additional cost of $$10$ for each room obtained at a neighboring hotel. If the goal is minimize the expected cost to XLRI, how many rooms should XLRI reserve at the convention hotel?

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