Question $1$

Armidale Tech Solutions sells Flash model laptops that cost $$562$ each and retail for $$998.$ Weekly demand averages $15$ units. The cost of placing an order with Flash is $$50,$ and the lead time is four weeks. The annual inventory holding cost rate has been calculated at $20$ percent. If the retailer is out of stock of the laptop, it estimates that it will suffer a combined cost of loss of goodwill and administration expense of $$10$ for each week that a customer must wait for the laptop to arrive.

Answer the following sub$-$questions:

$($a$)$ What is the optimal inventory policy for the laptops in terms of order quantity and reorder point? Explain the meaning of the reorder point you have calculated. $(4$ marks$)$

$($b$)$ How many calendar days between orders will there be$?(3$ marks$)$

$($c$)$ Calculate the total inventory cost and total annual profit of this policy. $(5$ marks$)$

$($d$)$ What percentage of customers will be placed on backorder? $(3$ marks$)$