Problem:
Brooks Inc., a boutique women's apparel retailer, is planning the production quantity for one of their silk blouses in Fall. They plan to sell the blouse for $150 and since they procure it from Asia, it only costs them $50 including transportation costs. At the price of $150, they expect to sell about 500 units but demand for a particular style is quite uncertain and they expect the demand to be normally distributed with a standard deviation of 200. Any items left over at the end of the Fall season are typically sold to an off-price outlet and they estimate they will get only $40.
(Q1) How many units of the silk blouse should Brooks order to maximize expected profits?
(Q2) What is the expected number of units that will be sold to the off-price outlet?
(Q3) Mr. Yuan Kwok, manager at Brooks, is not happy that they sometimes lose a lot of money because they order conservatively and demand for a blouse turns out to be greater than their purchase. He believes that, if they are stocked out, all of their customers (because they tend to be loyal) for this blouse will be willing to wait for the blouse for a few days and they could get the blouse produced locally in a few days but it will cost them a lot more -- $100 per blouse. Should they consider this option and, if yes, what will be the initial order quantity to their Asia supplier in this case?