Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 18

The Pedal Pusher Bicycle Shop operates 7 days per week, closing only on Christmas Day. The shop pays $300 for a particular bicycle purchased from the manufacturer. The annual holding cost per bicycle is estimated to be 25% of the dollar value of inventory. The shop sells an average of 25 bikes per week. Frequently, the dealer does not have a bike in stock when a customer purchases it, and the bike is back ordered. The dealer estimates his shortage cost per unit backordered, on an annual basis, to be $250 due to lost future sales (and profits). The ordering cost for each order is $100. Determine the optimal order quantity and shortage level and the total minimum cost.