The daily demand for a spare engine part is a random variable with a distribution, based on past experience, given by Number of Demands per Day Probability 0 .21 1 .38 2 .19 3 .14 4 .08 The part is expected to be obsolete after 400 days. Assume that demands from one day to the next are independent. The parts cost $1,500 each when acquired in advance of the 400-day period and $5,000 each when purchased on an emergency basis during the 400-day period. Holding costs for unused parts are based on a daily interest rate of 0.08 percent. Unused parts can be scrapped for 10 percent of their purchase price. How many parts should be acquired in advance of the 400-day period? (Hint: Let D1, D2, . . . , D400 represent the daily demand for the part. Assume each Di has mean  and variance 2. The central limit theorem says that the total demand for the 400-day period, Di, is approximately normally distributed with mean 400 and variance 4002.)