In the pursuit of happiness, Cooper sells Q-scanners to doctors. If necessary, he mail-orders the product from the supplier at the beginning of the week, and it takes him 3 weeks to receive the order. The weekly demand D is Poisson distributed, with mean ED = 1. If the demand cannot be satisfied immediately, it is backlogged and met as soon as the product is available.

(a) How many scanners does Cooper have in the mail?

(b) At any moment, Cooper decides to keep up to 6 Q-scanners at home or in the mail. What is the probability that Cooper can meet the demand immediately?

(c) If Cooper decides to keep up to 5 scanners at home or in the mail, how many Q-scanners does he have at home or in mail at the end of the week?

(d) If cooper wants to satisfy at least 70% of demand immediately, what is the Copper's target inventory position?