Cooper sells three types of eReaders-A, B, and C-at the same unit price $150. The weekly demand for each type is normally distributed with mean 750 and standard deviation 250. The demand for types A and B is negatively correlated, with correlation coefficient = -0.4; the demand for type C is independent of types A and B. The holding cost is 10% of the selling price per week.

(a) Cooper cares deeply about service quality. He targets the in-stock probability of 95%. He places orders every week, and the lead time from his supplier to his store is three weeks. What is the expected end-of-week inventory for each type of eReaders?

(b) Cooper decides to replace types A and B eReaders with a universal type U. The demand for types A and B will swtich to type U. All else remain the same. What is the expected end-of-week inventory for type U?