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?