Consider a workstation consisting of a single machine arrival rate of $1$ part per hour. Processing time is $0\mathrm{.}8$ hours per part, and lot setup time $($regardless of lot size$)$ is $4$ hours. The process is known to have moderate variability, and for sake of simplicity, variability is assumed independent of the lot size. More specifically, variability factor $($V$)$ is assumed $1.$

Lot size $($Q$)$ is desired to be optimized so that cycle time $($CT$)$ is minimized.

Part a $(12$ pts$.)$

Compute $($i$)$ optimal lot size, $($ii$)$ resulting cycle time, and $($iii$)$ resulting utilization for each of the following three cases $($summarize your results in a two$-$way table$)$:

$$ Original case

$20\%$ reduction of setup time

$20\%$ reduction of processing time