You are using a $1$ GHz system with paged virtual memory for doing a real$-$time application. No other application is running on the system. A real time application is one where each task must be finished within a guaranteed time bound. In this particular real$-$time application, there are many tasks; each runs the exact same code but with different data each time. Each real$-$time task reads $20$ bytes from an I$/$O device, performs some processing on it$,$ and writes the updated $20$ bytes of data back to the I$/$O device. I$/$O reads or writes are performed at $20$ MB$/$sec$.$ The code to process the $20$ bytes has a total of $10$ loads and stores, and takes $10000$ cycles when all memory accesses are cache hits. These loads and stores can access anywhere in virtual memory. The system transfers control to another task with an overhead of $1000$ cycles.

Every memory access takes $25$ ns and every disk page transfer from the virtual memory swap space takes up to $2$ ms$.$ In the worst case a load or store could require $4$ memory accesses and $2$ disk transfers. How many real$-$time tasks can be guaranteed to run on this system per second in the worst case? $($Assume the worst$-$case virtual memory behavior.$)$