Question $2$: $[25$ Marks$]$

On a day, six cars are awaiting the washing and waxing services at a car garage. Both the washing and waxing processes can serve one car only at a time.

The following table shows the times in minutes required to complete each of the six cars in the washing and waxing processes. Each car must follow the same sequence, beginning with the washing process and moving to the waxing process.

$\backslash$table$[[,$a$,$b$,$c$,$d$,$e$,$f$],[$Washing$,13,18,16,18,17,14],[$Waxing$,15,12,17,18,11,16]]$

a$.$ Determine a sequence that will minimize the makespan time.

$[10$ marks$]$

b$.$ Construct a chart of the resulting sequence, and find the optimal makespan, Washing process's idle time, Waxing process's idle time, and the total idle time of this two$-$machine flow shop.

$[15$ marks$]$