Response to the following problem:
Scott Stereo sells personal tape players. One of its more popular sellers is the Sonic Walkperson. These units cost Scott $18.55 each and retail for $32.95. Weekly demand averages 12 units. The cost of placing an order with Sonic is $25, and lead time is two weeks. Scott uses a 26% annual inventory holding cost rate. If Scott is out of stock of the Walkperson, it estimates that it will suffer a customer goodwill cost of $ 2 for each week a customer must wait for the Walkperson to arrive. A fixed administrative cost of $0.50 is associated with each backordered customer. Determine the following:
a. The optimal inventory policy (order quantity and reorder point) for the Walkpersons.
b. The number of calendar days between orders (cycle time).
c. The percentage of customers who will be placed on backorder.
d. The total annual inventory cost (holding, ordering, shortage, and procurement) for this policy and the projected total annual profit for this policy.