Stereo Goods is a distributor of videotapes. Video Mart is a local retail outlet which sells blank and recorded videos. Video Mart purchases tapes from Stereo Goods at $$100$ per tape. Video Mart does not inspect the tapes due to Stereo Goods' reputation for high quality. Annual demand is $(320$ days to be $6,400$ tapes$).$ The purchase$-$order lead time is $7$ days. The following cost data are available:

Relevant ordering costs per purchase order

$$64$

Carrying costs per unit per year:

Relevant insurance, materials handling,

breakage, etc., per year

$$2$

Required

Determine the economic order quantity

$(2$ marks$)$

Determine the appropriate level of safety stock, assuming stock out cost is $$1$ per unit and the following estimated demand. $($Assume a $10$ unit$-$interval for each safety stock level increments$)$

$\backslash$table$[[$Total Demand $($tapes$)$ during purchase order lead time,$120,130,140,150,160],[$Probability$,20\%,25\%,30\%,10\%,15\%$