$[15$ points$]$ Dan's Auto Detailing business performs two major activities: exterior cleanup, and interior detailing. Based on the size of car and condition, time estimates for six cars on Monday morning are as shown in the accompanying table.

$\backslash$table$[[,$Car Number$],[,1,2,3,4,5,6],[$Exterior$,35,20,40,30,25,45],[$Interior$,24,32,26,42,36,28]]$

a$.$ Sequence the cars so that exterior detailing is done first, and total completion time is minimized. What is the sequence of jobs? $($Hint: This is a tw$-$resource problem$)$

b$.$ Draw a Gantt chart to show the sequence of jobs.

c$.$ Evaluate the idle time for each activity. What is the total idle time?