n processes are time$-$sharing the CPU, each requiring T ms of CPU time to complete. The context switching overhead is S ms$.$

a$)$ What should be the quantum size Q such that the gap between the end of one quantum and the start of the next quantum of any process does not exceed M ms$?$

b$)$ For n $=5,$ S $=10,$ and M $=450,$ M $=90,$ M $=50,$ determine

$-$The corresponding values of Q

$-$The percentage of CPU time wasted on context switching