Suppose a retailer sees mean demand for a fashion item at 4000 units, with a co-efficient of variation of 20 percent. The purchase cost of the item (to the retailer) is $100, and if unsold the item is discounted and sold at 60 percent of the purchase cost. The item's list price is $150. There is also a goodwill penalty of $20 if the retailer runs short of the item. Lastly the retailer has to pay royalty to the designer of $25 for each unit that is sold. What is the optimal amount of inventory the retailer should order for this item