Bower is an outdoor clothing accessories chain that produces a line of hats for $10 from its Asian supplier, BowerSports. Unfortunately at the time of order placement, demand is uncertain. Bower forecasts that its demand is normally distributed with a mean of 2,100 and standard deviation of 1,200. The hats are sold for $22. Unsold hats have little salvage value: Bower simply donates them to charity. Note: Parts a) and b) have nothing to do with the newsvendor model and are simply probability questions using the Normal distribution.

a) The hat will be considered a dud if it sells less than 40 percent of the mean forecast. What is the probability the hat is a dud? Probability = ________________

b) Bower will consider this hat to be a big success if it sells more than 4,000. What is the probability it will be a big success? Probability = ________________

c) What order quantity, Q, maximizes Bowers expected profit? Q = ________________

For the remaining questions assume the order quantity Q = 3,000.

d) What are the expected lost sales? Expected Lost Sales = _______________ e) What are the expected sales? Expected Sales = ________________

f) What is the expected left over inventory? Expected Left Over Inventory = ________________ g) What is its expected profit? Expected Profit = _______________

h) What is the expected fill rate? Expected Fill Rate = ________________ i) What is its stock-out probability? Probability = ________________