When a new technology meets the requisite market potential, a new patent is filed. Patents are granted for a

period of $12$ years starting from the date of issue. Once the patent is filed, the new technology is developed at

one of its three independent development centers $($IDCs$)$ and is then launched to the market. Each product is

developed at only one center, and each center can only develop a single patented technology at a time. On

average, Pharma Dev files a new patent every $5$ months $($with standard deviation of $5$ months$).$ The average

development process lasts $12$ months $($with standard deviation of $24$ months$)$