The manager at Sportmart, sporting goods store, has to decide on the number of skis to purchase for the winter season. Based on past demand data and weather forecast for the year, management has forecasted demand to be normally distributed, with a mean of 300 and a standard deviation of 100. Each pair of skis costs $115 and retails for $290. Any unsold skis at the end of the season are disposed of for $95. Now, assume that it costs $5 to hold a pair of skis in inventory for the season, and the loss of goodwill is estimated to cost $20 per a pair of ski. (a) How many skis should the manager order to maximize expected profits?
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