Problem $1$

Consider an assembly line with $3$ sequential operations A$,$ B$,$ and C with processing rates $10,40,$ and $30$ parts per hour, respectively. Suppose there is one dedicated worker for A and B $($Abe$)$ and one dedicated worker for C $($Chris$).$ However, both workers are perfectly cross$-$trained.

HINT: The first step is to calculate the cycle times of operations A$,$ B$,$ and C$.$

$($a$)$ What is the process capacity in parts per hour?

$($b$)$ Suggest a way of reassigning tasks to Abe and Chris so as to maximize the process capacity. What is the maximum process capacity?

$($c$)$ What is the cycle time of the process on a day when Chris is absent$,$ and Abe is the only worker?