Case Scenario: The Krewe of Orpheus
The Krewe of Orpheus maintains a supply of swizzle sticks for events throughout the year. Demand for swizzle sticks is shockingly low, a quick check of krewe records from last year reveals that they used only 585,000, but the krewe president believes that they should be good stewards of what they have, so they seek to manage this inventory using the EOQ policy, although they prefer to refer to it as an EOKrewe policy for obvious reasons. Swizzle sticks are not expensive items, they cost a nickel apiece largely due to the club logo printed on each one. This also serves to increase the lead time as they can't be obtained from a standard restaurant supply house. Instead, they must be ordered with an eye towards the six-day lead time. It costs $15 to place an order, most of this cost is a result of explaining the meaning of "Laissez les bons temps rouler" and why it should be printed on the edge of each swizzle stick. Holding cost is 20% of purchase price.
The supplier offers the Krewe of Orpheus a deal; if they will buy at least 50,000 at a time, they will pay only 4.9 cents each, and if they buy at least 100,000 at a time, they will pay only 4.8 cents each. What is the total cost of the optimal order quantity?