The manager of the Quick Stop Corner Convenience Store $($which never closes$)$ sells four cases of Stein beer each day. Order costs are $$20\mathrm{.}00$ per order, and Stein beer costs $$8\mathrm{.}00$ per six$-$pack $($each case of Stein beer contains four six$-$packs$).$ Orders arrive three days from the time they are placed. Daily holding costs are equal to five percent of the cost of a Stein beer case.

If he were to order $16$ cases of Stein beer at a time, what would be the length of an order cycle?

Question $1$ options:

a$)3$ days

b$)4$ days

c$)1$ day

d$)0\mathrm{.}25$ days