A manufacturer uses a purchase part who's demand over any time period of length t (in years) can assume to be normally distributed with mean 200t and variance 400t. The part cost $20 each. The lead-time is 4 weeks. The annual carrying cost rate is 0.2 $/$/year. All shortages are backlogged and the shortage cost is proportional to the number units short, where the backlogged cost is $16 per unit. The setup cost is $100. A reorder point (s, Q) policy is used. (Assuming 52 working weeks within a year). a) Find the optimal order quantity and the reorder point. b) Find the average total relevant cost (setup cost, inventory holding cost and shortage cost)