An electronic device retail shop buys and sells Bluetooth speakers. The annual demand for speakers is normally distributed with mean 1500 and standard deviation 100. A speaker costs $250 to the shop and the annual interest rate is 25%. The shop pays $2500 for each order placed and an order arrives in 8 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 $40. (Assume a year has 52 weeks.)

a. [8 points] The electronic device retail shop applies (Q, R) control policy for Bluetooth speakers where Q = 500 and R = 300. Calculate the Type I and Type II service levels of this inventory control policy.

b. [12 points] Find the optimal order quantity, reorder point, and safety stock for Bluetooth speakers.

c. [5 points] What is the expected number of shortages when the optimal policy found in Part (b) is applied.