Problem $3$

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?