Consider a two$-$station line. The first station pulls from an infinite supply of

raw materials. Between the two stations there is a buffer with room for five jobs. The

second station can always push to finished goods inventory. However, if the buffer is full

when the first station finishes, it must wait until there is room in the buffer before it can start

another job. Both stations take $10$ minutes per job and have exponential process times

$($ce$=1).(25$ pt$)($Hint: Calculation$)$

a$)$ What are TH$,$ CT$,$ and WIP for the line? $($Use Eq $8\mathrm{.}38,8\mathrm{.}37,8\mathrm{.}39,8\mathrm{.}40,$ Little$$s Law to

compute TH$,$ Partial WIP, Partial CT$,$ Total CT$,$ Total WIP, $5$ pt$)$

b$)$ What are TH$,$ CT$,$ and WIP if we increase the buffer to seven jobs? $($Use the same

equations from a$),5$ pt$)$

c$)$ What are TH$,$ CT$,$ and WIP if we slow down the second machine to take $12$ minutes per

job? $($Hint: For unbalanced lines, u$=12/10,$ eq$\mathrm{.}8\mathrm{.}36,$ eq$.8\mathrm{.}35,8\mathrm{.}39,8\mathrm{.}40,$ Little$$s Law to

compute TH$,$ Partial WIP, Partial CT$,$ Total CT$,$ Total WIP, $5$ pt$)$

d$)$ What are TH$,$ CT$,$ and WIP if we slow down the first machine to take $12$ minutes per job?

$($Hint: u$=10/12,$ TH stays the same, compute TH$,$ Partial WIP, Partial CT$,$ CT$,$ WIP, $5$ pt$)$