. Consider a product produced from raw material using a single machine as shown in the figure below. The machine has production rate units per year and the product has a constant demand rate units per year. At the beginning of a production cycle a batch of raw material is delivered to the stocking point 1 from which the machine is directly fed. The output from this machine is immediately (unit for unit) transferred to stocking point 2 which faces the constant customer demand. The ordering cost of the raw material is = $300. The machines have setup costs =$50. The unit variable cost of the raw material is 3S. After being processed in the machine, the unit variable cost increases to 30S. The carrying charge has been established as 0.25 S/S/year. Assume one unit of raw material is used to produce one unit of finished good. Stocking Point 1 Machine I Stocking Point 2 Page 2 Prepared by P. M. Detersha Using graph, show the inventory history of both the raw material and that of the finished product. Write a total relevant cost expression and determine the optimal order quantity. . Taking the fact that the raw material has a larger ordering and a smaller unit carrying costs than that of the finished product, the production manager suggested that the order quantity of the raw material should be large enough to cover two consecutive production runs. Write a total relevant cost expression and determine the corresponding optimal order quantity following the suggestion of the production manager. Also determine the cost saving that may result by following his/her suggestion. (Using graph, show the inventory history of both the raw material and that of the finished product.)