A system adopts a priority$-$based preemptive scheduling wherein the priority of each process has been shown in the table below. In a recorded time$-$span, the system has seven processes, P$1,$ P$2,$ P$3,$ P$4,$ P$5,$ P$6$ and $P7$ as shown in the following table:

$\backslash$table$[[$Process ID$,$Priority,Arrival Time $($in ms$),$Total CPU Time $($in ms$)],[$P$1,1,t=0,13],[$P$2,3,t=8,12],[$P$3,5,t=12,5],[$P$4,2,t=17,8],[$P$5,4,t=23,7],[$P$6,2,t=36,17],[$P$7,6,t=52,9]]$

Assume that the dispatcher takes $2$ milliseconds for a process switch $($context switch$).$ Also assume that a process with a higher priority number has a higher priority. At a particular instance if you encounter any $2$ processes having the same priority then choose the one that arrived first.

A$)$ Draw a Gantt Chart $($Timing Diagram$)$ for the above data.

$(4$ points$)$

B$)$ Calculate the turn$-$around time for each process.

$(4$ points$)$

C$)$ Calculate the average turn$-$around time.

$(2$ points$)$