One of the products stocked at Weiss's paint store, is a certain type of highly volatile paint thinner that, due to chemical changes in the products, has a shelf life of only one year. Al Weiss purchases the paint thinner for $20 a gallon can and sells it for $50 a can. The supplier promises to buy back any leftovers for $8 for recycling.

Answer the following questions,

a A statistical study shows that normal distribution is a good fit to the sales data. The distribution has a mean 45 and a standard deviation of 7. What is the optimal ordering quantity? What is the minimum mismatch cost? What is the optimal expected profit?

b Another supplier of the same product approaches Al Weiss and offers a price of $15 a gallon can. However, this supplier cannot buy back any leftovers. Should Al Weiss switch to this supplier or keep the old one? Why or why not?