Elite Couture, a high-end fashion goods store has to decide on the quantity of Luella Bartley handbags to sell during the Christmas season. The unit cost of the handbag is $28.50 and the handbag sells for $150. All handbags remaining unsold at the end of the season are purchased by a discounter for $20 each. Further, there is a significant 40% inventory holding cost incurred for each unsold bag. Demand for bags is distributed normally with mean 150 and standard deviation 20. How many bags should be purchased to maximize expected profit?