A computer assembly plant assembles one of its computers C1 locally, and gets its main component, P1, from a local supplier. The weekly demand for the P1 is normally distributed with mean 90 and a standard deviation of 15. The company follows a continuous review policy. The supplier lead-time is 3 weeks. Every time the stock reaches a pre-specified Re Order Point (ROP), a lot of Q = 500 is ordered.

(a) If the Cycle Service Level is 95.0%, find the Safety stock, ROP, cycle inventory, and average inventory.

(b) Assume that the plant also assembles another model, computer C2. Its main component P2 is also supplied by the same supplier. P2 also has the same demand pattern, with weekly demand distributed normally with mean 90 and a standard deviation of 15. Supplier lead time is 3 weeks. For the same service level as above, find the total safety stock for both P1 and P2.

( c) If the company redesigns the computers in such a way that the same main part P1 can be used for both the computers C1 and C2, find the safety stock of the common component P1, for the same service level. Assume that the demands for C1 and C2 are independent.