One of O'Neills 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 1 30. 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 markdown.
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 = OAO, and yellow = 0.20.
a. Suppose O'Neill already has no extra small-tall Animals in stock. What is O'Neills 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 1 2.5 percent, then what now is its expected profit from the black Animal?