Isles Ltd require a kanban system for a specific part number AB$-12345-$AA which is going to be supplied by Gamma Ltd in containers, each of quantity $3.$ The weekly demand by day for this part number $($in units$)$ over the past six weeks has been as indicated in Table $6\mathrm{.}1$ and it has been agreed that the delivery frequency will be twice daily and the kanban signal will be via a $9$ am and Ipm daily email. Table $6\mathrm{.}1$: Demand for Part$-$Number AB$-12345-$AA by week for six weeks $\backslash$begin$\{$tabular$\}\{|$l$|$c$|$c$|$c$|$c$|$c$|$c$|\}\backslash$hline Day$/$Week &

$1$

&

$2$

&

$3$

&

$4$

&

$5$

&

$6$

$\backslash \backslash \backslash$hline Monday & $54$ & $61$ & $56$ & $73$ & $68$ & $67\backslash \backslash \backslash$hline Tuesday & $60$ & $70$ & $62$ & $68$ & $65$ & $55\backslash \backslash \backslash$hline Wednesday & $59$ & $59$ & $64$ & $62$ & $56$ & $72\backslash \backslash \backslash$hline Thursday & $73$ & $62$ & $66$ & $61$ & $59$ & $68\backslash \backslash \backslash$hline Friday & $56$ & $72$ & $55$ & $73$ & $61$ & $74\backslash \backslash \backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$ Weekly $\backslash \backslash$ Average $\backslash$end$\{$tabular$\}$ & $60\mathrm{.}5$ & $64\mathrm{.}8$ & $60\mathrm{.}7$ & $67\mathrm{.}7$ & $61\mathrm{.}9$ & $67\mathrm{.}4\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}$ The standard deviation of daily demand is equal to $6\mathrm{.}2$ units. The company allows

$20\%$

for safety stock and ideally it would like its buffer stock to accommodate a desired service level of

$97\mathrm{.}5\%$

$.(1)$ Calculate the maximum inventory level for AB$-12345-$AA at Isles Ltd$.(2)$ How many kanbans are needed?