You have just been hired by Pumper's, the pump manufacturer from previous weeks, to help them improve their inventory management. The managers have told you that your first priority should be to oversee the inventory control of a specific item, P$-052$K$,$ which has just seen a large increase in price. Since last year, the supplier of the item has been acquired by a competitor and increased the prices for certain items, including this one. As a result, in this year's contract, the item is purchased at $$12$ per item. Pumper's is currently using an policy for replenishment of P$-052$K$,$ where is found using the EOQ model. The annual demand for the item is $2,700$ units per year and the forecast for the next year shows an RMSE of $245$ units. The ordering cost is $$8$ per order. The current lead$-$time is constant at $7$ weeks. The holding cost is $20\%$ per year, and for each unit short there is a penalty cost of $$5.$ Pumper's takes ownership of the stock only when it arrives at its location. In your calculations, assume $50$ weeks per year. Calculate the parameters that should be used with the current inventory policy, using this year's purchase cost for P$-052$K $($$$12).$ What reorder point, s$,$ should you use? What economic order quantity, Q$,$ should you use? What are the expected total annual costs for item P$-052$K $($including purchasing, holding, ordering and shortage$)$ using the parameters in Part $1?$ Please round to closest integer dollars. What is the cycle service level associated with the policy in Part $1?$ Answer as a percentage with two decimals. Management has suggested that you might want to switch to periodic review, something the supplier of item P$-052$K was previously against but is now encouraging. You would review the inventory every $2$ weeks. If you switch to an $-$policy using the transformations from the lesson, what are the expected total annual costs? Please round to closest integer dollars. Answer without the dollar symbol. Which of the following statements is$/$are true about the two policies from Part $1$ and Part $4?$ Note that there may be more than one correct answer. Check all boxes that apply. The expected total annual cost is higher with the policy The safety stock level is higher with the policy The safety stock level is higher with the policy None of the above