Silvercrest Manufacturing Ltd$.$ is using Kanban containers. There are two

adjacent work centres, a downstream $($using$)$ and an upstream $($producing$)$

one. The using work centre has a production rate of $200$ parts per day and

each container holds $21$ parts. It takes $0\mathrm{.}5$ days for a container to make the

entire cycle from the time it leaves the upstream centre until it is returned,

filled with production, and leaves again. The manager wants a risk factor of

$20\%.$

i$.$ What is the maximum inventory of parts in the system?

ii$.$ If the company wants the number of containers $($holding $21$ parts each$)$

to be $5,$ what must the risk factor become?