A local boutique is planning orders for its $2024-25$ fall$/$winter catalog. One order will be placed nine months ahead of the selling season. For a formal dress they are planning to include in the collection, they think demand will be normally distributed with a mean of $40$ and standard deviation of $15.$ The store plans to sell the dress at a price of $$350.$ The supplier quoted a price of $$200$ per dress and logistics costs to bring the dresses to store add up to $$10$ per dress. Unsold dresses will be moved to a store that sells discount prom dresses at the end of the selling season and will be priced at $$180.$ It is assumed that at that price all remaining dresses will sell. It costs $$15$ to hold a dress in inventory until the end of the season and move it to the discount store. How many dresses should the boutique order? Please show your work.

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The boutique should order $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ dresses.