Consider the business process chart shown in Figure $2.$ The parenthesis gives, for each activity, the expected waiting time and the expected processing time in minutes in that order. Assume that the loop may be repeated only once if needed.

$($a$)$ Calculate the average cycle time of this business process.

$($b$)$ There are $10$ units of resource R$1,12$ units of resource R$2$ and $12$ units of resource R$3.$ Table $2$ shows the type of resource that each activity requires.

Activity Resource

A R$1$

B R$2$

C R$1$

D R$2$

E R$3$

F R$1$

G R$1$

H R$3$

I R$3$

J R$3$

K R$1$

Table $2$

$($i$)$ If $100$ jobs go through the process, what is the average time they spend at the work station where activity B is carried out?

$($ii$)$ What is the bottleneck of this business process?

$($iii$)$ If you are asked serve in one of the three resource groups, which one would you choose? Give reasons for your choice.