A specific raw material is consumed in a factory at a fairly steady rate of 60 per week. The raw material costs $2 each unit. It costs the factory $1200 to initiate, process and receive an order. Inventory holding costs are based on an annual interest rate of 25%. a. Determine the optimal order quantity and the optimal period of time (in terms of weeks) between placement of orders. b. Suppose that although we have estimated demand to be 60 per week, it turns out that it is actually 120 per week. (There is a 100% forecasting error). What percentage increase in total holding and ordering cost was caused by this 100% demand forecasting error? c. Suppose that the factory is considering to accept backorders. Having backorders at the raw material inventory may cause interruptions in the production plan, and thus each unit backordered per unit time costs $0.5. Consider the demand is 60 per week. What is the percentage savings in total holding and ordering costs compared to the case with no backorders?