3.2 (EOQ for MP3s) Suppose that your favorite electronics store maintains an inventory of a certain brand and model of MP3 player. The store pays the manufacturer $165 for each MP3 player ordered. Each order incurs a fixed cost of $40 in order processing, shipping, etc. and requires a 2week lead time. The store estimates that its cost of capital is 17% per year, and it estimates its other holding costs (warehouse space, insurance, etc.) at $1 per MP3 player per month. The demand for MP3 players is steady at 40 per week.

a) Using the EOQ model, calculate the optimal order quantity, reorder point (r), and average cost per year.

b) Now suppose that backorders are allowed, and that each backorder incurs a stockout penalty of $60 per stockout per year. Using the EOQ model with planned backorders, calculate the optimal order quantity, stockout percentage (x), reorder point (r), and average cost per year. How much money would the store save per year by allowing stockouts, expressed as a percentage?