ila Battle has determined that the annual demand for #6 screws is 1,000,000. Lila, who works in her brother's hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is 0.005 cent (not a typo). Assume that the demand is constant throughout the year. You can assume that the hardware store is open for 200 days in a year.

How many #6 screws should Lila order at a time if she wishes to minimize total inventory cost?

How many orders per year would be placed? What would the annual ordering cost be?

What would the average inventory be? What would the annual holding cost be?

It takes approximately eight working days for an order of #6 screws to arrive once the order

has been placed. The demand for the screws is fairly constant, and on average, Lila has observed that her brother's hardware store sells 500 of these screws each day. Because the demand is fairly constant, Lila believes that she can avoid stockouts completely if she orders the screws only at the correct time. What is the ROP?

Lila's brother believes that she places too many orders for screws per year. He believes that an order should be placed only twice per year. If Lila follows her brother's policy, how much more would this cost every year over the ordering policy that she developed earlier?

How would the optimal order quantity change if the ordering cost were $20, $30, and $40?