Response to the following problem:
Appliance Alley is a retailer of brand-name major appliances. One of its best sellers is the Poseidon brand washing machine. Demand for this machine averages 8 units per week. The machines cost Appliance Alley $625 each and sell for $999 each. Appliance Alley estimates that its annual holding cost rate for the washing machines is 18%. The cost of placing an order is $150, and the lead time is three weeks. If Appliance Alley is out of stock of the washing machines, it offers customers a discount of $5 for each day they must wait for their washing machine. The administrative cost of placing a customer on backorder is estimated to be $ 10.
a. What is Appliance Alley's optimal inventory policy for the Poseidon brand of washing machines?
b. If Appliance Alley follows an optimal inventory policy, what percentage of customers will have to wait for their washing machines?