One of the products stocked at Ms. Paige Turner’s paint store is a certain type of highly volatile paint thinner that, due to chemical changes in the product, has a shelf life of exactly one month. Ms. Turner purchases the paint thinner each month for $20 per can and sells it for $50 per can. The supplier buys back cans not sold during the month for $10 for recycling/reprocessing. Any excess demand during the month is lost revenue.
A) Suppose that the company wants to decide how many cans they should stock in order to minimize the expected total cost. What is the optimal service level that Ms. Turner should target to maximize expected profits?
B) Assume that Ms. Turner has approximated the probability distribution of monthly demand on the product with a normal distribution with a mean of 400 and standard deviation of 20 cans. What is the optimal order quantity (in # of cans) that Ms. Turner should submit to the supplier to maximize expected profits?