Question: One of the products stocked at Weiss's paint store, mentioned in Problem 14, is a certain type of highly volatile paint thinner that, due to chemical changes in the product, has a shelf life of exactly one year. Al Weiss purchases the paint thinner for $20 a gallon can and sells it for $50 a can. The supplier buys back cans not sold during the year for $8 for reprocessing. The demand for this thinner generally varies from 20 to 70 cans a year. Al assumes a holding cost for unsold cans at a 30 percent annual interest rate.
a. Assuming that all values of the demand from 20 to 70 are equally likely, what is the optimal number of cans of paint thinner for Al to buy each year?
b. More accurate analysis of the demand shows that a normal distribution gives a better fit of the data. The distribution mean is identical to that used in part (a), and the standard deviation estimator turns out to be 7. What policy do you now obtain?