One of O'Neill's high-end wetsuits is called the Animal. Total demand for this wetsuit is normally distributed with a mean of 200 and a standard deviation of 130. In order to ensure an excellent fit, the Animal comes in 16 sizes. Furthermore, it comes in four colors, so there are actually 64 different Animal SKUs (stock-keeping units). O'Neill sells the Animal for $350 and its production cost is $269. The Animal will be redesigned this season, so at the end of the season leftover inventory will be sold off at a steep mark- down. Because this is such a niche product, O'Neill expects to receive only $100 for each leftover wetsuit. Finally, to control manufacturing costs, O'Neill has a policy that at least five wetsuits of any size/color combo must be produced at a time. Total demand for the smallest size (extra small-tall) is forecasted to be Poisson with mean 2.00. Mean demand for the four colors are black 0.90, blue 0.50, green 0.40, and yellow 0.20.
a. Suppose O'Neill already has no extra small-tall Animals in stock. What is O'Neill's expected profit if it produces one batch (five units) of extra small-tall black Animals?
b. Suppose O'Neill announces that it will only sell the Animal in one color, black. If O'Neill suspects this move will reduce total demand by 12.5 percent, then what now is its expected profit from the black Animal?