Question $2$

We have a process as shown in the right figure. $($M$1-$M$4$ are the names for four machines. The numbers are activity times in minutes$).$ Consider the following schedule:

Schedule a job on M$1$ every $10$ minutes, starting at time $0$; schedule a job on M$2$ every $5$ minutes starting at time $0.$ Jobs finished on M$1$ go to M$3$; jobs imisieu vir ivic gu tu ivis.

a$)$ Plot this schedule for the first $6$ jobs in the following Gantt chart. The first job and the $\backslash (4^\{\backslash$text $\{$th $\}\}\backslash )$ job start on M$1.$ The second, third, $\backslash (5^\{\backslash$text $\{$th $\}\}\backslash ),$ and the $\backslash (6^\{\backslash$text $\{$th $\}\}\backslash )$ jobs start on M$2.$ The first block of job $1-5$ is plotted for you.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & & $91$ & $10$ & $11$ & $12$ & $13$ & $14$ & $15$ & $16$ & $17$ & $18$ & $1$ & & $20$ & $21$ & $22$ & $23$ & $24$ & $25$ & $26$ & $27$ & $28\backslash \backslash$

$\backslash$hline M$1$ & $1$ & & & & & & & & & & & $\backslash [$

$4$

$\backslash ]$ & & & & & & & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline M$2$ & $2$ & & & & & $3$ & & & & & & $5$ & & & & & & & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline M$3$ & & & & & & & $1$ & & & & & & & & & & & $\backslash [$

$4$

$\backslash ]$ & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline M$4$ & & & $2$ & & & & & $3$ & & & & & & $5$ & & & & & & & & & & & & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

You can extend the above chart as needed.

b$)$ Find the WIP on each machine and complete the below table.

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|\}$

$\backslash$hline Machine & WIP $($units$)\backslash \backslash$

$\backslash$hline M$1$ & $\backslash \backslash$

$\backslash$hline M$2$ & $\backslash \backslash$

$\backslash$hline M$3$ & $\backslash \backslash$

$\backslash$hline M$4$ & $\backslash \backslash$

$\backslash$hline Total WIP & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$