An electronic device retail shop buys and sells Bluetooth speakers. The annual demand for speakers is normally distributed with mean 3000 and standard deviation 60. A speaker costs $100 to the shop and the annual interest rate is 20%. The shop pays $1000 for each order placed and an order arrives in 4 weeks. Any demand that is not satisfied on time is fully backordered and the penalty cost incurred by not satisfying a customer demand on time is estimated to be $50 (Assume a year has 52 weeks.) a. [6 points) Find the optimal order quantity, reorder point and safety stock for speakers b. [6 points) What are the service levels (Type I and Type II) obtained by the policy in Part(a)? c. 19 points) What would be the optimal order quantity, if the annual demand was deterministic and constant with mean 3000 and no backorders were allowed. What would be the annual cost of inventory holding and ordering costs in this case? d. 19 points) Based on your answer in Parts (a) and (c), what is the cost of uncertainty in demand to this company