Please show all formulas used!!!!!!!!!!

Case #5 Inventory Management Background Zhou Bicycle Company (ZBC), located in Seattle, is a wholesale distributor of bicycles and bicycle parts. Formed in 1981 by University of Washington Professor Yong-Pin Zhou, the firm's primary retail outlets are located within a 400 -mile radius of the distribution center. These retail outlets receive the order from ZBC within 2 days after notifying the distribution center, provided that the stock is available. However, if an order is not fulfilled by the company, no backorder is placed; the retailers arrange to get their shipment from other distributors, and ZBC loses that amount of business. The company distributes a wide variety of bicycles. The most popular model, and the major source of revenue to the company, is the AirWing. ZBC receives all the models from a single manufacturer in China, and shipment takes as long as 4 weeks from the time an order is placed. With the cost of communication, paperwork, and customs clearance included, ZBC estimates that each time an order is placed, it incurs a cost of $65. The purchase price paid by ZBC, per bicycle, is roughly 60% of the suggested retail price for all the styles available, and the inventory carrying cost is 1% per month ( 12% per year) of the purchase price paid by ZBC. The retail price (paid by the customers) for the AirWing is $170 per bicycle. ZBC is interested in making an inventory plan for 2023 . The firm wants to maintain a 95% service level with its customers to minimize the losses on the lost orders. The data collected for the past 2 years are summarized in the following table. A forecast for AirWing model sales in 2023 has been developed and will be used to make an inventory plan for ZBC. 2. How many times should orders be placed throughout the year? How often should orders be placed? Hint: assume 300 working days per year. 3. What is the reorder point, assuming safety stock will be included? 4. What are the total costs of inventory? 5. Bonus Question: Trace the inventory balance over the course of the year. Assume starting inventory balance of 35 bicycles. Also assume that retail orders are called into ZBC the first business day of every month and the first order to ZBC suppliers is on Jan 4, 2023. Hint: Take into consideration orders to suppliers and supplier lead time, orders from retailers and lead time in shipments to retailers, as well as the estimated time between orders to suppliers. Consider creating a table such as: What conclusions or recommendations do you draw from tracing the inventory in step 5 ? Case #5 Inventory Management Background Zhou Bicycle Company (ZBC), located in Seattle, is a wholesale distributor of bicycles and bicycle parts. Formed in 1981 by University of Washington Professor Yong-Pin Zhou, the firm's primary retail outlets are located within a 400 -mile radius of the distribution center. These retail outlets receive the order from ZBC within 2 days after notifying the distribution center, provided that the stock is available. However, if an order is not fulfilled by the company, no backorder is placed; the retailers arrange to get their shipment from other distributors, and ZBC loses that amount of business. The company distributes a wide variety of bicycles. The most popular model, and the major source of revenue to the company, is the AirWing. ZBC receives all the models from a single manufacturer in China, and shipment takes as long as 4 weeks from the time an order is placed. With the cost of communication, paperwork, and customs clearance included, ZBC estimates that each time an order is placed, it incurs a cost of $65. The purchase price paid by ZBC, per bicycle, is roughly 60% of the suggested retail price for all the styles available, and the inventory carrying cost is 1% per month ( 12% per year) of the purchase price paid by ZBC. The retail price (paid by the customers) for the AirWing is $170 per bicycle. ZBC is interested in making an inventory plan for 2023 . The firm wants to maintain a 95% service level with its customers to minimize the losses on the lost orders. The data collected for the past 2 years are summarized in the following table. A forecast for AirWing model sales in 2023 has been developed and will be used to make an inventory plan for ZBC. 2. How many times should orders be placed throughout the year? How often should orders be placed? Hint: assume 300 working days per year. 3. What is the reorder point, assuming safety stock will be included? 4. What are the total costs of inventory? 5. Bonus Question: Trace the inventory balance over the course of the year. Assume starting inventory balance of 35 bicycles. Also assume that retail orders are called into ZBC the first business day of every month and the first order to ZBC suppliers is on Jan 4, 2023. Hint: Take into consideration orders to suppliers and supplier lead time, orders from retailers and lead time in shipments to retailers, as well as the estimated time between orders to suppliers. Consider creating a table such as: What conclusions or recommendations do you draw from tracing the inventory in step 5