Problem
The Pedal Pusher Bike Shop operates seven days a week, closing only on Christmas day. The shop pays $300 for a particular bicycle purchased from the manufacturer. The annual holding cost per bike is estimated at 25% of the dollar value of the inventory. The shop sells an average of 25 bikes per week. Frequently, the dealer does not have a bike in stock when a customer requests it and the dealer back orders it. The dealer estimates his shortage cost per unit back ordered, on an annual basis, to be $250 due to lost future sales. The ordering cost for each order is $100.
Determine the following:
i. Optimal order quantity.
ii. Optimal Shortage level.
iii. Total minimum cost.
iv. Time between orders.