$3.$ Consider the example covered during Class session $3$ on $$Risk Pooling Across Locations,$$ and answer the following questions:

a$)$ What is the average inventory of product B in NJ and MA$?(15$ points$)$

b$)$ Assuming that the demand for product B across the MA and NJ locations are independent. Now if we centralize the warehouses for product B$,$ what is the average inventory of product B at the centralized warehouse? $(15$ points$)$

c$)$ How much inventory reduction we get by having a centralized warehouse for product B$?(5$ points$)$