Please show work & formulas in Excel - thanks!

Problem 3 (12 points) Gary Simon, manager of a large warehouse in Sioux Falls makes procurement decisions for industrial flood lamps carried by the warehouse. The throughput rate of lamps through the warehouse is 2500 units per day. The demand varies randomly with a standard deviation of 500 lamps per day. Gary places an order for 62,500 lamps whenever the inventory level falls below 24,000. It takes a fixed 9 days for the order to arrive. The cost of purchasing the flood lamps is $5 per lamp. The cost of placing the order is $1,000 per order. The holding cost is 10 percent of the purchase price per lamp per year. Consider 250 working days in a year. a. What is the size of the cycle inventory associated the current inventory policy? b. What is the reorder point (ROP) for the current policy? c. What is the size of the safety stock in the current policy? d. What is the overall average inventory is for the current policy? e. What is the standard deviation of the lead time demand? f. What is the service level corresponding to the current inventory policy? Problem 4 (8 points) Consider the business scenario from problem 3. Now, Gary wants to implement an optimal inventory policy with a desired service level of 97.5 percent. All other data remain the same. a. What order size should Gary adopt? b. What reorder point (ROP) should Gary adopt? c. What is the annual inventory holding cost for the optimal policy