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.

a. A retired operations management professor moves to New Orleans, joins the Krewe of Orpheus and convinces krewe leadership to buy their own swizzle stick production equipment. They invest in a medium-scale machine called the Swizzo 2025, which is capable of producing swizzle sticks at the rate of 1800 per day. What is the optimal batch size?

b. What is the average inventory if they order at their EOKrewe quantity?