Question: Shakina Harris, who works in her brother's hardware store, is in charge of purchasing. Shakina has determined that the annual demand for #6 screws is 150,000 and is fairly constant over the 200 days that the store is open each year. She estimates that it costs $30 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 0.6 cents.

(a) How many #6 screws should Shakina order at a time?

(b) It takes 8 working days for an order of #6 screws to arrive once the order has been placed Because the demand is fairly constant, Shakina believes that she can avoid stockouts completely if she orders the screws only when necessary. What is the ROP?

(c) Shakina's brother believes that she is placing too many orders for screws each year. He believes that orders should be placed only twice per year. If Shakina follows her brother's policy, how much more would this cost every year over the ordering policy that she developed in part (a)? If only two orders are placed each year, what effect would this have on the ROP?

(d) Shakina now believes that her estimate of an ordering cost of $30 per order is too low. Although she does not know the exact cost, she believes that it could be as high as $60 per order. How would the optimal order quantity in part (a) change if the ordering cost were $40, $50, or $60?