$6-21$ It takes approximately eight working days for an order of number $6$ screws to arrive once the order has been placed. $($Refer to Problem $6-20.)$ The demand for number $6$ screws is fairly constant, and on average, Lila has observed that her brother$$s hardware store sells $500$ of these screws each day. Because the demand is fairly constant, Lila believes that she can avoid stockouts completely if she orders the number $6$ screws only at the correct time. What is the ROP? $6-22$ Lila$$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$$s policy, how much more would this cost every year over the ordering policy that she developed in Problem $6-20?$ If only two orders were placed each year, what effect would this have on the ROP? $6-23$ Barbara Bright is the purchasing agent for West Valve Company. West Valve sells industrial valves and fluid control devices. One of the most popular valves is the Western, which has an annual demand of $4,000$ units. The cost of each valve is $$90,$ and the inventory carrying cost is estimated to be $10\%$ of the cost of each valve. Barbara has made a study of the costs involved in placing an order for any of the valves that West Valve stocks, and she has concluded that the average ordering cost is $$25$ per order. Furthermore, it takes about two weeks for an order to arrive from the supplier, and during this time, the demand per week for West valves is approximately $80.($a$)$ What is the EOQ? $($b$)$ What is the ROP? $($c$)$ Is the ROP greater than the EOQ? If so$,$ how is this situation handled? $($d$)$ What is the average inventory? What is the annual holding cost? $($e$)$ How many orders per year would be placed? What is the annual ordering cost?