(Inventory Management: Newsvendor Model) Redmond Plant Shop (RPS) sells a particular type of carnivorous plant called Venus Flytraps, with the majority of the sales made in the spring months. RPS makes a one-time purchase of the Venus Flytraps prior to each spring season at a cost of $8 each and sells each Venus Flytraps for $15. There is also a transportation cost of $4 for each Venus Flytraps, since they are bought in North Carolina and shipped across country for sale in Redmond, Washington. Any Venus Flytraps unsold at the end of the spring season is marked down to $3 and sold at a special summer sale (assume all marked-down Venus Flytraps are sold). a) The demand during spring months is estimated by a market research company to be normally distributed with mean 1,000 and standard deviation 600. Calculate the optimal quantity of Venus Flytraps RPS should purchase.
b) Instead of the estimated normal distribution by the market research company, RPS now decides to use its own demand statistics which have been collected over several years. The empirical probability of demand is summarized in the following table Demand 400 500 600 700 800 900 1000 1100 1200 1300 1400 0.01 0.03 0.05 0.06 0.10 0.15 0.20 0.20 0.12 0.05 0.03 Probability Given the above empirical probability of demand, find the optimal quantity to purchase (i. e., the Newsvendor solution).