Frankfurt Electronics produces a component internally using a state-of-the-art technology. The operations manager wants to determine the optimal lot size to ensure that the total annual inventory cost is minimized. The daily production rate for the component is 500 units, annual demand is 36,000 units. The manager estimates that the total cost of a finished component is $80. The annual holding rate is 30 percent of the finished component cost. Setup cost for each production cycle is $150 per setup, and if we assume that the plant operates year-round, and there are 360 days per year, find a) The optimal production lot size, b) Based of result of a), i. what is the highest inventory level? ii. What is the average inventory level, and annual inventory cost? iii. What are the # of production runs in each year, and annual setup cost? iv. Calculate the annual total costs on holding, setup, and cost of component production, v. length of each production period, vi. length of each inventory cycle, vii. rate of inventory buildup during the production cycle, viii. the number of inventory cycles per year? c) Plot the movement of the inventory during one production cycle using time on the horizontal axis and on- hand inventory on the vertical axis d) Discussion: i. if the speed of component production increases, whether or not the optimal average inventory will increase, why? ii. If the production setup cost decreases, whether or not the optimal average inventory will increase, why?