Quick Print Inc. uses plain and three-hole punched paper for copying needs. Demand for eachpaper type is highly variable. Weekly demand for the plain paper is estimated to be normallydistributed with mean 100 and standard deviation 65 (measured in boxes). Each week, areplenishment order is placed to the paper factory and the order arrives five weeks later. Allcopying orders that cannot be satisfied immediately due to lack of paper are back-ordered. Theinventory holding cost is about$1 per box per year. Quick Print estimates that the backorderpenalty cost is $20 per box. Assume that there are 4.33 weeks per month. Required:
What is Quick Print’s optimal target inventory position for plain paper if Quick Print operates with a 99 percent in-stock probability?