Sam has set up his own e-commerce venture called HUJI-BagZone. He sells genuine leather handbags handmade by Italian artisans in Italy. He has been able to streamline the manufacturing processes, thanks to the Operational skills he learnt in the operations course. His per unit cost of production (including manufacturing and labor costs) is $100. His venture is quite new and in a unique space. As such, there is very high uncertainty in the demand. Sam forecasts the demand to follow a Normal distribution with a mean of 50,000 units and a standard deviation of 15,000 units. He also decides to sell off any left-over inventories at a steeply discounted value of $50 in the local market. Sam decides to sell the bags at a unit price of $200. Now Sam is faced with a difficult question of manufacturing the right quantity of bags that maximizes the profit in face of uncertainty of demand. (a) What should be the quantity of the bags manufactured by Sam to maximize profits