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.
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?