A FMS consists of three stations plus a load$/$unload station. Station $1$ loads and unloads parts using two servers workers$).$ Station $2$ performs horizontal milling operations with two servers $($idential CNC horizontal milling machines$),$ vertical miltin $3$ operations with three servers $($identical CNC$,$ vertical milling machines$).$ Station $4$ performs driling operations $($identical drill presses$).$ The machines are connected by a part handling system that has three work carriers and a mean transportstion time is $3\mathrm{.}5$ and the operation frequency is fijk$=1\mathrm{.}0$ for all opeartions.

Given that the required production is $10$ parts per hour, distributed according to the product mix indicated in Table $1.$

$($i$)$ Find the minimum number of servers at each station and the minimum number of carts in the transport sstem that are required to production demand,

$($ii$)$ Find the utilization of each station for the answers above, and

$($ii$)$ comment on the results

$\backslash$table$[[$A$,\backslash$table$[[$Palloxiph$],[02]],\frac{\text{Q}\text{a}\text{r}\text{i}\text{t}\text{i}\text{n}\text{k}\text{.}}{1},\backslash$table$[[$Dscription$],[$lead$]],$Cetani,$\backslash$table$[[$Processtarth$],[$Imin$]]],[,2,$nunn,$2,13$ mis$],[,3,$vail,$3,14$ in$],[,4,$Onil,$4,$II mas$],[,5,$uxloed,$1,],[$n$,0\mathrm{.}2,1,$land,$1,4tan$