Total Mark: $100$ points, Date: $7/12/2023$

Time allowed: $60$min $($including submission time$)$

Q$\mathrm{.}1$: $(40$ pts$.)$ A thirteen$-$station rotary$-$indexing machine performs machining operations at twelve workstations, and the thirteenth station is used for unloading and loading parts manually. The longest process time on the line is $1\mathrm{.}8$min and the unloading$/$loading operation requires less time than this. It takes $15\mathrm{.}0sec$ to index the machine between workstations. Stations break down with a frequency of $0\mathrm{.}009,$ which is considered equal for all stations. When breakdowns occur, it takes an average of the first$-$right digit of your student number plus $4$ min to diagnose the problem and make repairs. In addition, the cutting tools on the stations need to be changed every $160$ cycle; this takes $16$min for all stations in total. The starting work part costs $$3\mathrm{.}50$ per unit. Operating cost of the indexing machine is the first$-$right three digits of your student number in dollars $$,$ and tooling cost is $$0\mathrm{.}5$ per piece. Determine

$($a$)$ Line cycle time

$($b$)$ Line efficiency,

$($c$)$ Average hourly production rate, and

$($d$)$ Cost of finished part.