Amazon sells 3 types of books A, B, and C at the same price per unit of $150. The weekly demand for each is normally distributed with a mean=750 and SD=250. the demand for A and B are negatively correlated p=-0.4. the demand for C is independent. The holding cost is 10% of selling price per week.

1. The target in stock probability is 95% orders are placed every week and lead time from supplier is 3 weeks. what is the expected end of the week inventory for each type of book?

2. Amazon decides to replace A and B with a universal type U book. the demand for A and B will switch to U. all else remains the same. what is the expected end of the week inventory for type U?