BestTech is a local electronics store. You are asked to determine the optimal ordering policy for AM$07$ Tower Fan. The weekly demand for this tower fan is normally distributed with a mean of $75$ units and standard deviation of $10$ units. The store follows the continuous review EOQ model to manage its inventory. BestTech orders AM$07$ Tower Fan from the supplier at a unit cost of $$200$ and the fixed ordering cost of $$180.$ The annual cost of carrying a unit of inventory at the store is equal to $30\%$ of the unit cost. It takes $2$ weeks to receive a delivery. Assume that a year has $52$ weeks.

$($Note: $z$ values corresponding to standard normal probabilities may be calculated using Excel of the table provided at the end of page $3)$

a$.$ Compute the Economic Order Quantity that BestTech should use.

b$.$ Compute the safety stock $($units of tower fans$)$ needed to maintain a service level of $95\%.$

c$.$ What is the annual holding cost for carrying this safety stock?

d$.$ Compute the reorder point for $95\%$ service level.

e$.$ How much additional safety stock would be needed if BestTech wishes to increase the service level from $95\%$ to $98\%?$ What is the additional cost associated with this increase in the safety stock?

Table of z$-$values

$\backslash$table$[[$Probability$,$z$-$value,Probability,z$-$value$],[0\mathrm{.}99,2\mathrm{.}326,0\mathrm{.}89,1\mathrm{.}227],[0\mathrm{.}98,2\mathrm{.}054,0\mathrm{.}88,1\mathrm{.}175],[0\mathrm{.}97,1\mathrm{.}881,0\mathrm{.}87,1\mathrm{.}126],[0\mathrm{.}96,1\mathrm{.}751,0\mathrm{.}86,1\mathrm{.}080],[0\mathrm{.}95,1\mathrm{.}645,0\mathrm{.}85,1\mathrm{.}036],[0\mathrm{.}94,1\mathrm{.}555,0\mathrm{.}84,0\mathrm{.}994],[0\mathrm{.}93,1\mathrm{.}476,0\mathrm{.}83,0\mathrm{.}954],[0\mathrm{.}92,1\mathrm{.}405,0\mathrm{.}82,0\mathrm{.}915],[0\mathrm{.}91,1\mathrm{.}341,0\mathrm{.}81,0\mathrm{.}878],[0\mathrm{.}90,1\mathrm{.}282,0\mathrm{.}80,0\mathrm{.}842]]$