Quick Print Inc. uses plain and three-hole-punched paper for copying needs. Demand for each paper type is highly variable. Weekly demand for the plain paper is estimated to be normally distributed with mean 100 and standard deviation 65 (measured in boxes). Each week, a replenishment order is placed to the paper factory and the order arrives five weeks later. All copying orders that cannot be satisfied immediately due to the lack of paper are back-ordered. The inventory holding cost is about $1 per box per year.
a. Suppose that Quick Print decides to establish an order-up-to level of 700 for plain paper. At the start of this week, there are 523 boxes in inventory and 180 boxes on order. How much will Quick Print order this week?
b. What is Quick Print's optimal order-up-to level for plain paper if Quick Print operates with a 99 percent in-stock probability?