Question: Semicon is a start-up company that produces semiconductors for a variety of applications. The process of burning in the circuits requires large amounts of nitric acid, which has a shelf life of only three months. Semicon estimates that it will need between 1,000 and 3,000 gallons of acid for the next three-month period and assumes that all values in this interval are equally likely. The acid costs them $150 per gallon. The company assumes a 30 percent annual interest rate for the money it has invested in inventory, and the acid costs the company $35 a gallon to store. (Assume that all inventory costs are attached to the end of the three-month period.) Acid that is left over at the end of the three-month period costs $75 per gallon to dispose of. If the company runs out of acid during the three-month period, it can purchase emergency supplies quickly at a price of $600 per gallon.

a. How many gallons of nitric acid should Semicon purchase? Experience with the marketplace later shows that the demand is closer to a normal distribution, with mean 1,800 and standard deviation 480.

b. Suppose that now Semicon switches to a 94 percent fill rate criterion. How many gallons should now be purchased at the start of each three-month period?