$1.(20$ points$)$ Refer to Figure $4\mathrm{.}3$ in your textbook or Slide $12$ of Lecture $5.$

$($a$)$ Identify the bottleneck activity on this operation process chart.

$($b$)$ What is the cycle time for the bottleneck activity?

$($c$)$ Calculate the number of teakettles that can be produced in an $8-$hour shift with $400$

minutes available time, assuming that one worker is assigned to handle each production

activity such as operation, inspection, and assembly.

$($d$)$ Show the efficiency of each worker based on the cycle time calculated from $($b$).$ Explain

why this is not an efficient way $($i$.$e$.,$ one worker per activity$)$ to produce teakettles.