Tim Madisen$18\mathrm{.}3-3.$ Tim Madsen is the purchasing agent for Computer Center,

a large discount computer store. He has recently added the hottest

new computer, the Power model, to the store's stock of goods. Sales

of this model now are running at about $13$ per week. Tim purchases

these computers directly from the manufacturer at a unit cost of

$$3,000,$ where each shipment takes half a week to arrive.

Tim routinely uses the basic EOQ model to determine the

store's inventory policy for each of its more important products. For

this purpose, he estimates that the annual cost of holding items in

inventory is $20$ percent of their purchase cost. He also estimates that

the administrative cost associated with placing each order is $$75.($a$)$ Tim currently is using the policy of ordering $5$ Power model

computers at a time, where each order is timed to have the

shipment arrive just about when the inventory of these com$-$

puters is being depleted.

annual costs being incurred with this policy.

find the optimal order quantity by applying the EOQ formula by hand.

$($II$)$ With the optimal order quantity obtained above, how fre$-$

quently will orders need to be placed on the average? What

should the approximate inventory level be when each order is

placed?

$($g$)$ How much does the optimal inventory policy reduce the

total variable inventory cost per year $($holding costs plus

administrative costs for placing orders$)$ for Power model

computers from that for the policy described in part $(a)?$

What is the percentage reduction?