$7\mathrm{.}5.$ Consider a four$-$station line in which all stations consist of single machines. Station $2$ has

average processing times of $2$ hours per job, while the remaining stations have average

processing times of $1$ hour per job. Answer the following, under the assumption that process

times are deterministic $($as in the best case$).$

$($a$)$ What are $$ and $0$ for this line?

$($b$)$ How do $$ and $0$ change if a second identical machine is added to station $2?$ What

effects will this have on performance?

$($c$)$ How do $$ and $0$ change if the machine at station $2$ is speeded up to have average

processing times of $1$ hour? What effects will this have on performance?

$($d$)$ How do $$ and $0$ change if a second, identical machine is added to station $1?$ What

effects will this have on performance?

$($e$)$ How do $$ and $0$ change if the machine at station $1$ is speeded up to have average

processing times of $1/2$ hour? What effects will this have on performance? Do your results

agree or disagree with the statement $$An hour saved at a non$-$bottleneck is a mirage $($i$.$e$.,$ of no

value$)?$