SUPPORT Manufacturing produces widgets using a multi$-$stage production process. The process consists of three main stages: A$,$ B$,$ and C$.$ Each stage has a different processing time. The processing times $($in minutes per unit$)$ for each stage are as follows: Stage A: $10$ minutes; Stage B: $15$ minutes; Stage C: $20$ minutes. The firm operates two $8-$hour shifts per day and seven days per week.

a$)$ Calculate the capacity per week for each stage. $($Ans: A$,672$; B$,448$;$,336)$

b$)$ Determine the bottleneck stage in the production process. $($Ans: C$)$

c$)$ Calculate the maximum achievable production rate per week. $($Ans: $336)$