Selin sells high-end road bikes in Pasedena, California. She has established a contract with Specialized to their Amira bike in her store and Specialized requires that she does not stockout of their Amira bikes. Specialized charges $289 per order plus $1000 per bike ordered. Because these are specialty bikes, Specialized takes a while to fill the orders, but guarantees that any order placed will arrive exactly 2 months later. Selin estimates her annual holding cost to be $90 per bike. She estimates that she will sell 15 Amira bikes each month.
a) How many bikes should Selin order so that she minimizes her average total cost per year?
b) How frequently should she place an order?
c) At what inventory level should Selin order bikes so that she does not run out. That is, what is her reorder point?